I don't think anyone here is arguing that other factors don't play a significant role, including both other equipment, rendered frame rates, and player skills, preferences and training. None of that takes away from the fact that, all else being equal, a higher refresh rate allows for faster reaction times and smoother motion tracking. Of course, all else
is very rarely equal, and no two LCD panels have identical characteristics, let alone when comparing between panel technologies. OLED has unbeatable pixel response times, which for some people might be preferable to a higher refresh rate LCD with slower response times even at a lower refresh rate. All of these factors are tightly interconnected, so nothing you can read off a spec sheet (or even an in-depth review) will give any type of definitive answer - especially as user perceptions are highly contextual and variable, especially over time. I've never used a 240Hz (or higher) monitor, and I kind of doubt I ever will - I don't play those types of games, and other factors matter more to me. The main "benefit" of such a high refresh rate would likely be to highlight how poor my reaction times and aim are
And there are of course diminishing returns as you go higher, as the Hz-to-ms ratio gets ever smaller - 60 to 120Hz goes from 16.7 to 8.3ms - a reduction of over 8ms and as such a major change, but on the other hand going from 240Hz to 360Hz is just a 1,39ms reduction from 4,167 to 2,778ms. The proposed future high-end refresh rate of 480Hz is an even smaller 0.7ms reduction. So while these changes
are perceptible, and
can give an advantage given that the player has sufficiently fast reaction speeds and training to make use of this faster perception, the gains are ever smaller, and the benefits are ever more specialized.