If the camera shoots 4K then you'd be silly not to, and I was really looking for the smallest 1080p camera, not the smallest 4K camera, but I did include a couple for reference so that's my fault for not being clear.
I guess really this thread was a bit of a fantasy that I could trade spec for size, but we all know that's not how it works.
Even 10 years ago the tech was there to make a camera with a GoPro sized body and a P&S lens on the front. I have one of my daughters old cameras - a Fujifilm J20 from 2009, which is an SD P&S but it's just under 20mm / 0.79 inches thick and has a 3x optical zoom lens.
This is the J20 pictured with a fake SJ4000 action camera, which is basically the size of a GoPro.
Combine these and they could have make a 1080p camera with 3x optical zoom in a body thinner than a GoPro and by making it slightly wider they could have made room for the battery and given a little grip to hold it with.
Given that it might have been a big seller back then, I was hoping they'd be a forgotten classic and around for a couple of hundred, but really it's just a fantasy.
The idea is the "smallest 720p or 1080p P&S camera" not the "highest resolution P&S camera".
Sensible people don't want the best specifications available in the camera so large they can only just operate it, they want the nicest possible shooting experience with a camera that has the spec they need for their given situation.