When I was still using a 580 on my gaming rig, I would drop GTA and BeamNG to 1440p because having less input lag felt so much better than staying on 4k. 120fps to me is always noticeable but it really matters in speed based games, and FPS is really not the only genre where reaction times matter.
As someone that has been playing VR for 7 years now, 90hz stable vs 90hz average is the difference between a good and bad experience. I can see how people wouldn't mind input lag, given I grew up playing ps1 and N64, but at the same time its 2024 and gaming really is just so much better than it was before.
But even in slow games, normal turn based games like CIV or XCOM, camera movements and animations are still so much smoother than they ever were at 60hz. Its not like thats a big deal but its still always visible
I just wanna bring this back around to input lag, because since I started gaming at high refresh rates several years ago, I have really begun to appreciate having a game respond to my inputs in real time. I think maybe all those years growing up playing games at 30hz on old unoptimized hardware really makes me appreciate having inputs match what I see on screen 1:1. I find it to be a lot like driving a car, if my steering wheel had slop while I am on the highway I feel much less confident in my ability to drive. Or like, if my legs were springs, walking down stairs would be a lot harder.
TL;DR: if you can't see the difference between 60hz and 120hz you have messed up your display settings and the monitor actually isn't at 120hz, or you have very special eyes.