How old are you? I'm convinced this is an important detail.

I hosted a LAN party when I was in my early twenties when higher hz monitors were getting more popular in specifically the gaming scene. My buddy and I were playing a match of Counter Strike together side by side, me at 60Hz and him at 120Hz. I used to think like you, but it blew my mind how smooth it was in comparison, so much so I ordered a new monitor that weekend. I don't think it improved my ability to play in any significant way but it definitely felt nicer and smoother. Conversely, at the time you had to specifically set the option in Windows to account for higher Hz and if I forgot to on a reinstall or for whatever reason, I could tell something was off and would question my FPS and turn my counter on to see if I was getting lower FPS. You may not believe it, but I would noticably play worse. I thought it was psychosomatic myself until it happened a handful of times.

Now, I'm not a pro CS player by any means, but I guarantee you it matters, makes a difference, and is noticeable. I'm getting older now and care less as time goes on, but I still swear by and game on a high Hz monitor. When I look over my wife's shoulder on her low Hz monitor, the mouse movements are like a flipbook and when gaming on a Nintendo Switch 2 at 60 FPS, it is laughably noticeable.