The mistake with focusing on reaction time is that humans can anticipate actions and can perform complex sequences of actions pretty quickly (we have two hands and 10 fingers). So someone playing one of those "test your reaction time" games might only score like 30ms. But someone playing a musical instrument can still play a 64th note at 120BPM.

Imagine playing a drum that took between 0 and 5 extra frames at 60FPS between striking the head and it producing a sound. Most people would notice that kind of delay, even if they can't "react" that quickly.

In games, frame delay translates to having to hold down a key (or wait before pressing the next one) for longer than is strickly necessary in order to produce an effect. Since fighting games are all about key sequences, the difference between needing to hold key for 0 frames and 5 frames is massive when you consider key combinations might be sequences of up to 5 key presses. 5 frames of delay x five sequential key presses x 8ms a frame = 1600ms vs 1 frame x 5 seq. key presses x 8ms = 40ms.

There's a massive difference between taking 1.6s to execute a complex move and 0.040s.

Another example is music (and relatedly, rythm games). With memorized music you have maximal anticipation of actions. The regular rithm only amplifies that anticipation. Musicians can be very consistent at timing (especially rithm section), and very little latency or jitter can throw that off.

It's something you can get used to. A concert pianist can have 2-3 notes chasing each other down his/her arm. Myelinated nerve fibres are fast (the physiology is really interesting), but still has limits. Latency is more important for organists. Firstly, some instruments can have a delay of up to half a second for some ranks (a rank is a set of pipes - there can be one or more ranks per stop). Secondly, in any church of appreciable size, there will be a significant delay between when you press a key and when you hear the congregation singing the note. In fact standard advice is to ignore the congregation, otherwise you can end up slowing down as a reaction to the latency.

So for the second problem, you just ignore input and play "open loop". For the first problem, you may have to play notes on the slow rank slightly early, although this is only practical if you separate them off on a different keyboard. Otherwise, you can only use that rank for slow music, and make use of the note increasing in volume and changing in tone as that rank comes in.

Frame perfect moves are exceedingly common in most top fields. Just watch any video about the latest speedruns.

The thing with latency is it needs to be consistent. If your latency is between 3 to 5 frames you blew it because you can't guarantee the same experience on every button press. If you always have 3 frames of latency, with modern screens, analog controls, and game design aware of those limitations, that's much better. Look at modern games like Celeste, who has introduced Coyote Time to account for all the latency of our modern hardware.