The limit of human vision at whole-screen distances is somewhere between 1440p and 4k; we can err toward 4k just due to the absolutely batty sub-pixel arrangements used by OLED makers, but really, you're not getting much more out of it.
And not just because your eyes can't see it, again at comfortable whole-screen viewing distances, but also if you could see the content on a per-pixel level, you wouldn't be able to pay attention to it at all. This is why good 1080p content is almost indistinguishable from low-bitrate 4k content, for motion content at least.
It's a little different on computer monitors, both for desktop use and for gaming. Here you are close enough to focus on a small area of the screen and details matter. But we'd still put 8k down as the upper limit of single-user single-screen scenarios*, as the extra resolution does nothing for the user aside from requiring more horsepower to run.
(*once you start having multiple screens, with or without multiple viewers, more resolution can be helpful, but really only at larger sizes and closer than full-display viewing distances, where essentially viewers are cropping into the viewable area)
en.wikipedia.org
