It's a question of how you look at a display. Our color vision is lousy, which is the reason why we have movies with 23.97 frames/second.

But our peripherial vision are excellent at picking up movements even if it can't see color and is lousy at detecting details. A high frame rate is needed to avoid seeing flicker in the corner of your eye.

Next thing is that 50 or 60Hz are mains frequencies in different parts of the world. With some lamp technologies, the lamps will flicker at two times the mains frequency. And you don't want to have frame rates too close to this, because the difference between the two frequencies is much lower. So you can get interference frequencies that is very visible when surrounding lamps are on - but a flickerfree in sunlight or at night when surrounding lamps are off.

On TV transmissions, you have probably seen a black bar gliding over older CRT monitors. It's an example of the interference and out-of-phase capture of CRT data by a camera. But similar effects is causing us to notice flicker when both display and surrounding illumination are modulated.