Aliasing is vary easy to notice even on a 4k screen. Look at the second immage it's got way to much white and you can easily have the same issues at 4k or 8k.
http://en.wikipedia.org/wiki/Aliasing
In the end increasing resolution does help in most cases, but with the right fractal pattern there is no 'safe' resolution.
PS: It's basically the same reason that QuickSort is a O(n^2) sorting method in the worst case. Pick the wrong data and your assumptions fall apart.
Your points are more about refresh rates, video compression and lightning. For example, in gaming antialising and other "smoothing" techniques are wildy used to improve image quality, but when playing in 4K resolution on a 24inch screen you wouldn't need those anymore because your eye can't see a difference.