Worse, sometimes games don't even allow for a custom setting, where all there is for you to choose is just the preset settings that the game has provided for you. When that happens, all you can do is simply hope that the game is well optimized.

60 for the longest time. Then I spent about a year on 165 and the difference was indescribable. And finally moved on to 240 because the 165 display had pretty bad image quality. Still noticed a difference between 165 to 240 in a very fast paced game like UT but nowhere near as major as from 60 to 165.

I very much doubt I would notice going from 4.16ms per frame to 2.77ms if I went from 240 FPS to 360 FPS for example. The diminishing returns become insane the higher the framerate compared to refresh time goes, not to mention that cutting down that additional 1.4ms would require at least 50% more hardware power :P

The 240 Hz display cost me almost $900 bucks back in February 2020, but honestly, investing into a thing you will be starting at for very long periods of time is well worth it. Didn't regret it for a second, especially once I saw it in action. Even wrote a review for it here on the forums:
https://www.gog.com/forum/general/monitor_lenovo_legion_y27gq25

Ah I see. I always believed that beyond 60 fps there would be little to no improvement in how you play the game, so I guess I was wrong. Initially, my assumption was that you were playing the game at a framerate that's even below 60.

You do notice the difference - I went from a 60hz monitor to a 144hz G-sync one and while it might not "look" that different, there's a lot in the "feel" and responsiveness. But yes, it's diminishing returns.

From an accessibility standpoint, I really struggle where the framerate isn't a constant in terms of the refresh rate. So, let's say you've got a 50hz monitor - I can deal with 25fps and 50fps (although 25fps now feels much too slow for me), but I can't deal with frames being delivered at say 40fps or an inconsistent rate between the two. Basically, I get migraines from it, so always had to try to have settings to deliver a consistent full refresh rate or half refresh rate fps. With G-sync, having frame delivery tied to a dynamic refresh rate has all but eliminated headaches from playing games. I still get headaches from gaming on a laptop (which doesn't have G-sync or other adaptive sync technology), but never from my main PC monitor.

Anything that runs below 30 FPS doesn't even get my time of day anymore. I've spent more than enough time with sub-optimal frame rates with not powerful enough hardware in the mid-to-late '90s and most of the 2000s. I'll never put up with that again.

My preference is still 60 FPS overall. While I actually have a monitor that can do up to 120hz and my 2060 SUPER can run games at that speed if they're not the most demanding/newest, I still limit all games to 60 FPS. Yes, overall gameplay might be a bit smoother from what I've tried, but I can do without the extra heat, noise, and electricity use. 60 is my sweet spot for power/efficiency. Also, some games tend to go haywire (hello Skyrim!) if running at higher frame rates than that thanks to the poor decision of tying one's game logic to how fast it is running.

49 frames per second, my first low was 16 fps in early 90s and then 22 fps in 1996

I have a 144hz gaming laptop. Was playing resident evil 2 remake at 144 fps. The difference was little. As you said, I cap it at 60fps to lower heat and noise. On my Desktop PC, everything is a cap at 75fps because my monitor is 75hz.