Suppose two players notice each other at the same time (e.g. as would naturally happen when walking around a corner in a shooter), first to shoot wins, and their total latencies are identical Gaussians with a standard deviation of 100ms. Then a 6.5ms reduction in latency is worth an additional 2.5% chance of winning the trade. Maybe you won't notice this on a moment by moment basis, but take statistics and its impact should be measurable.
In ELO terms a 2.5% gain in win rate is around a 10 point increase (simplifying by assuming that single Gaussian is the entire game). That's small, but if you were a hardcore player and all it took to raise your ELO by 10 points was using a better monitor/mouse/OS... why not? Doing that is cheap compared to the time investment required to improve your ELO another 10 points with practice (unless you're just starting).
Also, I think you'd be surprised what people can perceive in a context where they are practiced. Speed runners hit frame perfect tricks in 60FPS games. That's not reaction time but it does intimately involve consistent control latency between practice and execution.