Nonsense, with all due respect.
That’s a massive overgeneralization and honestly pretty misleading.

Yes, there are a handful of games where physics or logic were historically tied to framerate. Everyone knows the classic examples. But acting like most games break at high FPS, even modern ones” is just flatout wrong and like already mentioned, very misleading.

Modern AAA and AA engines (Unreal, Unity, RE Engine, Snowdrop, Decima, etc.) are explicitly designed to decouple game logic from rendering. High refresh rate and high FPS have been standard targets for years now because of esports, VR and high-end PC gaming. If games were routinely breaking above 120 FPS, high-refresh monitors wouldn’t even be a thing.

The Wolfenstein II example gets brought up all the time but that’s one edge case, not the rule and it was patched. Same for games like F04. Cherry picking a rare bug and presenting it as evidence that high FPS is a major issue doesn't make any sense.

Are there some games with caps or weird behavior? Sure.
Are they most games? Not even close. You can literally count them on one hand compared to the thousands of titles that run perfectly fine at 144, 240, or higher FPS.

So no, high refresh and high FPS aren’t the problem.
Bad engine decisions or legacy code are.

If you’re going to make claims like this in a hardware forum, at least back them up with more than one outdated anecdote.
What is your source? How did you come up with this?

few games are timed to game speed and refresh/fps

if you are having problems with a specific game, ask in the games forum

for high fps it also takes a faster cpu
cpu prepares the frame, gpu draws them
most of the time, if the gpu is not at 95% or higher the cpu is holding it back

I recall that time delay loops etc were used to control speed in some games but I've not heard of that kind of thing since the appearance of Win 95, todays machines are vastly superior to what we had back then.

many console games from the 90s to early 2000s had the game speed tied to fps
ps1/ps2 ntsc (60i) games ran faster than the pal (50i) version
i would not doubt that many nes or sega analog console games did that too