Yeah, once you go sufficiently stopped down you get fewer cues that funky optics are involved, in the sense of a still image. I still think you get a different sense of perspective and spatial relationships between objects that's different than that of a spherical lens though, revealed through Z-axis movement. I think the cues end up "feeling" different even if you were to match horizontal FOV with an equivalent spherical lens.
I haven't tested this theory out though. Yet. I think to do it right you would have to use something like a 5D with spherical lens compared to a smaller format camera with an anamorphic lens, matching FOV and comparing both the still composition as well as depth cues from the camera dollying forward.
But, yeah, anamorphic and spherical are mixed in big motion pictures. You have a better than 50/50 chance that any film with heavy visual effects the photography containing the effects will be spherical, either shot on Super-35 or VistaVision. Most facilities don't like working with anamorphic plates when adding visual effects, unless a filmmaker mandates that no spherical photography is used even for effects plates.
This goes back to Star Wars at least. One of the first things Luc Besson was convinced to do at the beginning of The Fifth Element was to shoot spherical. Unfortunately. Nowadays with disc and RAM and CPU like we have there is less of a worry because working with the higher resolution imagery isn't a big deal and you can do optics compensation for tracking.
The Dark Knight Rises is another example of mixed photography, with anamorphic 35mm for most of the regular narrative parts of the film and 65mm for the big action set pieces.
We discuss mixed format subjects often with shooters and editors. It's usually fine to mix spherical with anamorphic now a days. It used to be a big NO WAY. Scott Pilgrim vs The World and Spring Breakers come to mind as 2 recent big budget projects that did a lot of mixing.