You can buy [1] polarization cameras, both mono and with a Bayer filter. They're expensive right now, but I agree it would be really cool to see what could be done with a consumer grade version in a smart phone.
Interesting. From what I can find the pixel format is 4 polarization directions per pixel, 45 degrees apart. Even though there are 4 channels this doesn't allow to deduce the V Stokes parameter (this camera can't capture circular polarization). Technically one channel is redundant here, but I guess it can be useful for reducing error.
I wonder if an alternative pixel format, with 3 polarization directions 60 degrees apart and a circular polarization channel would be desirable for some applications.
[1] https://thinklucid.com/product/phoenix-5-0-mp-polarized-mode... (among many others)