Reaction time is unrelated to perceptible latency. You're not reacting to things; you are seeing the result of an action you requested. You already know it's coming. To say that delays less than your reaction time don't matter is like saying it doesn't matter if your flight is delayed by an hour because it takes 8 hours to cross the Atlantic.
Watching your own hand movements through your phone camera is a good demonstration of this. Set 60 Hz video mode, and the latency is probably less than 30 ms - but still extremely obvious.
it's quite a lot more than 30ms, as phone cameras do some real heavy-weight image processing to compensate for their tiny size, I'm talking neural networks and such. the throughput might be 60fps when it's all conveyor-ed but the latency sure isn't