From far enough away anything looks good. If you look at the THX recommendations for cinema setup, they add up to something like a 60 degree viewing angle on the screen. To match human eye resolution you want approximately one pixel every 0.3-0.4 arc minutes; let's say 3 pixels / arc minute, or 180 pixels/degree. So for a screen that was "perfect" up to the limits of human perception, taking up a cinema-screen-sized area of your vision, you'd need at least 180*60~=10000 horizontal pixels.

We're approaching the limits of human perception, but we're not there yet; 4K does seem like a useful improvement over 1080