SRV1981

I agree (having owned 10 of their hybrid cameras and 2 camcorders in the last 15 years).
Panasonic has a long heritage in professional video (going back over 60 years) and it shows. I think the GH5 became a very popular camera for video because it was a good all-round, reliable, video tool in most situations, rather than excelling in any particular area at the expense of others or having a specific SOOC 'look'. 
For a bit of fun, this is 9 year old, basically SOOC, FHD 50p video from a Panasonic LX7 'enthusiast compact' with a small 10MP 1/1.7" sensor. There's some obvious aliasing/jaggies and I think the reds/oranges in particular are exaggerated. But for a camera launched in 2012 that fitted in the palm of one hand and weighed 270g I think it is reasonably decent (and could be improved in post). SOOC video from a G6, GX85 or G80 would leave it in the dust though, having much less aliasing and better balanced colours.
 

Post. I trust my calibrated monitor in a controlled room better than the one on set. So what I do with any new camera is I do a bunch of tests to find a setting that I like, then I shoot everything in that setting and adjust in post as needed. That way I am very familiar with what I can or can't do with that setting. I will often do tests to create specific color node graphs ahead of time, designed to be applied in post. But on the shoot I want everything to be familiar, even when I know based on my tests what it will transform into. That's not to say I'm good at cinematography. But I do think I'm good at not wasting people's time. I test everything ahead of time by myself or with the people leading the project, then we maximize set time for the actors and crew. No fiddling with settings while people are waiting around.

What I like about recent Canon C line is that the skin often has a bit more separation from other colors. I don't know that I prefer red/magenta, but it's not nice if skin gets muddled with everything else. I wouldn't say all Canon, because I was honestly never a fan of the C100's image for the few shoots I used it on.
I don't know that I especially like color on the Panasonic S-series as SOOC it tends to exaggerate yellows. It's a great camera and does what I need at an unbeatable price though.

Great camera.  It's cinema in a box the size of a pack of cigarettes.
There's nothing wrong with video - technically it's what I do.
One thing that is starting to be understood is the look of the footage, which with video often looks quite artificial, which is in contrast to film which looks quite organic.  Artificial isn't a bad thing either - all styles are valid.
My own preferences are for something that is aesthetically pleasing, mildly flattering, and doesn't call attention to itself.  This has pushed me into investigating the whole subject and what "cinematic" actually means, which leads into the territory of YouTubers making cinematic videos that despite having huge amounts of effort and thousands of dollars of equipment are some of the least cinematic videos ever made, even when compared to something like a T2i.
...and you can install your own.  Bingo!  Instantly, you can have whatever look you want, SOOC.
This is what I do.
My current best answer is GX85, 14-140mm zoom, 12-35mm zoom, and 12-32mm zoom.  If I'm not allowed to colour grade it, I'll edit it on a 720p timeline and export upscaling that timeline to 4K.  That will knock the digital edge off it.
Why?  
Because if your camera is large then you'll get beautiful images with lovely colour science and everyone in the background of those images will be staring at the camera.
Oh darn it!  There I go again, talking about something other than colour.  It's like I'll never learn that there's no more to film-making than camera tests.
C300mk2.
Why?
Go watch any video on why this is the most popular documentary camera.
Rent an Alexa.
If you want to understand why, go watch any video from a professional cinematographer or colourist talking about why Alexa is the best choice.
Neither do I.  Which is sort of the point I've been making all along.
Alexas are known to be green, sometimes even problematically so.  Canons are magenta.  etc etc.
If we're talking about choosing cameras for the best SOOC colour, and yet bizarrely there isn't any limitation on the fact that some cameras require 3 people to operate them, then I'm thinking that if you can put a LUT in the camera then it counts as being SOOC colour.  Ironically, because it comes SOOC lol.
In which case, you can choose Alexa 65 and just put a modified 250D / 2383 LUT in there and you're done!
Alexas also tend to go green.
There's a knob in any NLE that corrects this, but don't let 3s of work in post stop you from changing your entire set design around that one tiny little thing!

Right, but they are not the same as shooting log and then using Resolve color management as a 1-step modification. On my S5, shooting Vlog and then using color management > shooting standard profile.
Or, if you mean a baked in user-specified LUT, that adds another dimension again.
I know, I meant for the discussion. Otherwise... Alexa 35 is always the answer 🙂
These are hard questions because almost no test footage on the internet is SOOC, I haven't used every camera, and also of course there are many different film stocks so it really depends what you consider a film look. I'll also assume price new so the C70 is >$4k etc.
But given my limited knowledge, and if the only consideration is color with zero post manipulation, for a generic project, my only answer is the Samsung NX1. Absolutely blows everything else I've used out of the water!
However, I would never use NX as its a dead system with no active EF adapters. And there is no log profile.
So my personal choice in that scenario would probably be a Panasonic S5IIx. But a good portion of my reasoning is based on Vlog, its pixel shift photo mode, and no strange crop factors and other limitations like some others. So not strictly color.
This introduces another caveat in addition to the ones above, which is that color is the last consideration for a run and gun doc. My choice is whichever camera has the best AF, IS, sensitivity, audio, and reliability. So while the NX1 color is great, it's absolutely my last pick for the purpose.
Overall, I would pick a C200 for the $4k budget, and C500mkII for $10k. They have great color and also fit the other criteria.
Ergonomics play much less of a role here than for doc, but of course the big consideration is what the production looks like and what our goal is. Are we shooting natural light? Studio lights? Indoor with a couple 100-200W LEDs? What lenses? Since I can take my time, I'm absolutely shooting log and doing color work in post. So I wouldn't even consider the SOOC question for this scenario 🙂
For $5k I'm probably using a Z Cam F6. The ergonomics, sensitivity, and wireless control are huge, and the color is fine.
For $10k the C500mkII looks pretty good. My friend just got a pair and loves them, but I haven't tried it personally.

The budget is just for the body and not for the body+glass?
1) Used GFX 100S - the video is good enough for vacation and the stills are incredible
2a) C70 - looks nice SOOC, built-in ND's, nearly the perfect camera for a fast turn-around
2b) GFX 100 II (Love mine)
3a) C70 - as before and the raw from it is flexible enough for anything I do
3b) Used Monstro 8K VV - I haven't actually shot with one, but they seem pretty nice and I sometimes consider doing some trade-in toward one - used models are now about 6k for the brain on reputable used sites

Yeah I heard the original question, and I think that while the posts diving into complex grading are fascinating and useful to those of us who do post, I know that getting good color SOOC is a separate question.
One big point about your question is that it doesn't break down by manufacturer. Not all REDs look the same, not all Sonys look the same, etc. I think the Sony FX6 looks fine, but I dislike the FS7. Also, most cameras have different profiles. Sometimes, there is greater  difference between profiles on the same camera, than between normal/natural/standard/default/whatever profiles on many different cameras. And even within a profile, you'll have totally different results based on how many controls you leave on auto (such as WB) and your lens.
SOOC and minimal grading are completely different. SOOC excludes log profiles, for one thing.
There is budget as well. Best SOOC ever? Alexa 35, probably. Under $10k? C500mkII gets my vote. Under $2k? Nikon Z6 is solid. Are you including lenses in your budget? I like the color out of my Canon L 24-105 better than that of my Canon 50 1.8 (tested on Sony A7rII). Though I have also used terrible lenses for specific scenes, specifically to make them less appealing.
If you want a specific answer or even a specific discussion, ask a more specific question because your original question is extremely open ended--which is fine to start with! But it's probably more useful and interesting to narrow the parameters a bit.

For my own stuff, I prefer it to be as 'faithful as possible' to the original scene, within the limits of the tools I've got and the amount of time I'm prepared to spend fiddling with it. I don't care what someone else wants to categorise that as, but I suspect it would come under your 'video' category.
Personally the parts of the production process I find most interesting are being out-and-about recording the content, the basic editing (the clip choice, 'flow' and the cutting) and getting the best out of the ambient sound. Adjusting the image doesn't usually get much more advanced for me than brightness, contrast, saturation and sharpness, unless there's a clip that's particularly 'off' what I think it should look like in the lighting conditions at the time.
But I'm perfectly happy respecting and enjoying other peoples artistic choices, including abstract art (which is inherently non-realistic). But nobody likes every piece of art they view...

You do realize technology matters? You do realize different camera produce differences in image that are pleasing to some and not others? Do you realize the original thread is about what camera you prefer to get the closest to your goal image with minimal work? Are you aware 99% of responses didn’t address that? Should I wear makeup?

You can agree or disagree or bump whatever threads you want - I showed you examples from the real world.
If bumping threads somehow changed reality, I'd bump as many threads as was necessary to make it so that I could get Hollywood level colour from my phone without any work in post.  Hell, I'd create all the accounts and make all the posts myself if it would actually make it so.
I am so vocal about this because what you are asking about is what I desperately want, but that just isn't how it works.
To answer your question directly, no I don't say that the camera doesn't matter at all, but the camera doesn't matter in terms of getting great shots straight-out-of-camera without any work in post, because none of them can do it.  Have you ever seen ungraded Alexa footage?  It looks just like ungraded footage from any other capable camera (S1H, BMPCC, etc).
In fact, you know what...  here's your answer.  The BMPCC 4K.
Here is a comparison between an Alexa and a BMPCC 4K without any grading done in post except the ARRI LUT (and of course the BMPCC4K has had a conversion put onto it to make it match the Alexa).
Juan is a professional film-maker / colourist and this is the real-deal, not a YT LUT bro product.  
If you think that any camera is capable of what you want then the Alexa must be, and as you can see, with that conversion the BMPCC4K can do it too.
This is the product page.
https://juanmelara.com.au/products/bmpcc-4k-to-alexa-powergrade-and-luts
Knock yourself out!

The image I posted with the bad lighting was GH5, shooting LOG, with a standard conversion to 709.
The GH5 is a huge capable camera, the issue was the lighting not the camera.

Sure.
You just have to hope that the world is perfect and doesn't give you mixed lighting.  That every shot you take has the same lighting ratio.  That your camera doesn't have metameric failure as the WB changes to match the lighting changes.  Etc Etc.
Even on completely controlled film sets, colourists still tweak each shot to even them up between angles etc, so even if the world was perfect your results still wouldn't be.

....and if that image doesn't illustrate the problem with lighting, how about this one.
SOOC HLG:

With a basic grade:

These lights all looked white in person!
I sat down, pulled out my camera (GH5 again), looked through the viewfinder and was stunned at the green/magenta mess the camera saw.

More examples of bad lighting.
This was a 709 shot from my GF3, which obviously couldn't auto-WB far enough to compensate (yes, this looked white in person):

My best attempt at grading in post also couldn't compensate well enough:

But the real demonstration is on a project.
Here's a camera test I shot.  These are the images after grading:

They all look pretty straight-forward, but it took a lot of work to get to that.  Here are the shots SOOC:

Note that adjacent shots have considerably different looks - SOOC:

After:

Obviously I've let the flaring lower the contrast on the middle images to a certain extent because otherwise it would look too forced, but the tint of the first image and second ones needed to be evened out as one had the sun in it and the other didn't.
I've shot these tests by the beach many times, using many different cameras (OG BMPCC, BMMCC, GH5, GX85, XC10, GF3, iPhone, GoPro, etc), shooting manually and in auto, in RAW / LOG / 709, etc etc.  All required decent amounts of work in post to even them out and look normal.
It's like anything - the natural look takes the most amount of work and is, in reality, the least natural.
You keep saying you want nice looking images without doing any/much work, but I've been working super hard at this for quite some years now and it's just not possible.  You either get nice looking images with work, or you wave the camera around and you get out what you put in - a film that looks like a dad with a handycam.
The myth that you can buy it was created by equipment manufacturers trying to sell you cameras and LUT bros on YT trying to sell their LUT packs.

Clearly great points. But I think it’s still missing the mark, given that the user in my scenario wants a quick turn around in many lighting conditions outside of our control what sensors currently produce an image you love with minimal effort. 
 
the gx85 image is lovely but also the kids skin looks deathly anemic. Another sensor and processor would.l render that scene differently.  That’s the conversation 

I debated between the two last year and went with the C70.  It's my go-to A camera these days with the R5 as B camera.  Without watching that video, I'd guess that the image on the right is the C70 (more highlight and shadow detail).

I'm sure I posted it back then too. ML Raw is easy on the 5D3 due to dual card slots and its stability.
I'm sure the FX3 and R5C could get close... minus the 14bit color... but they're $3500 cameras and I already own the 5D3. 

I remember this ! it was posted here years ago! I remember trying ML and was blown away how good it looked but how hard it was to use. I think the fx3/r5c can give those looks now. 

And I'd be remiss if I didn't post this video from a British filmmaker named Paul Cook. It was the video that made me buy my 5D3 and install ML Raw on it and never look back. After 7 years, I'm still chasing what he was able to capture in an afternoon...
 

The first few scenes on the train felt like a movie. Loved it! In another thread I bumped from 2015 where folks discussed cameras and color, as is my goal, some commented that as brands have moved to mirrorless they’re chasing resolution and in doing so neglecting color and overall image. Something to the effect that chasing greens versus other colors, has had a negative impact on the way color is rendered and that’s 9 years ago. Worth a review that thread. 
 
I originally curious about modern cameras that produce that movie look in the first video without lighting makeup etc. the skin tones and overall look felt less digital and more movie like. That’s what I was getting at with what brands are trying to achieve that ? What models most of us can purchase today gets us to that. 

When I did the music video for that band a couple of months ago - it was a nightmare, but at the same time had me thinking - this just feels so right and so much what I want to spend my time doing. If only I didn't have to make a living!

Script and partial shortlist written. Ready for action tomorrow night when wife is out, so hopefully no interruptions!

I agree. His Sony work does not respond to me, neither in the edit, premise, lengthyness, choice of focal lengths, camera movement nor framing nor color palette and contrast. @mercer That Sigma 30mm is a thing I had been keeping in my mind. I am a sucker for 28mm on S35. Kendys Canon work was magic, his Sony uploads on his channel are video imo. Besides colour, movement, framing and lensing are not in the same league as his Canon library imho. I can relate to the impact of a camera on freewheeling video essay work. I still hold a G70 in high regard for the mojo it has in HD 24p. The only two pieces I shot with it are still oozing color magic and forced me to design my shots and movements instead of gimbleing through the world rather effortlessly. No effort means no magic in most of the instances.

Whenever I start thinking about the beginning of the DSLR revolution or the Digital Revolution, I take my own advice and go back to look at some old videos that I love from those forgotten cameras.
This first round of films, from Kendy Ty and his t2i, I have linked to countless times, years ago, but I think they could be helpful or relevant to the OP's topic...
If I remember correctly, he used the t2i and the old Sigma 30mm 1.4. I believe he even created his own picture profile, in camera, for his earlier films.
Like so many others, he eventually moved onto a Sony 4K camera, but many people commented they preferred the look from his trusty, old t2i.
If there's a lesson here, it's simple... sometimes less is more. Sometimes the tool that gets the job done and is simple to work with, is better than wading through the minutiae of features and tech finding the best camera.

Didn't know that was in B&W. Thanks for the heads up. I adore B&W, so much so that I've been testing my FP in 4K 8bit mode for the sole purpose of having a smaller set up for a B&W film.