That's much closer but not exactly the same as the kind of game and musical scenarios I'm discussing. That sounds more like a "singular" or "relatively rarely repeating" pattern/game.
In TrackMania fullspeed tracks and music, the predictable patterns repeat so often that after warming up you get much better in accuracy.
It takes me usually 1-3 hours of warming up (after days/weeks of not playing) to play keyboard at <10 ms accuracy, this is sort of similar to TrackMania, where if I kept weeks/months of break, I wouldn't perform well enough in my favorite tracks* without some warm up play. (*unable to reach finish due to error accumulation which reduces the window of opportunity to time the action accurately in the "full acceleration/speed required" tracks)
I hate tracks that can't be finished unless you play them flawlessly. I want to be able to do the first run really really slowly and horrible just to get a feel of where I'm supposed to go, and then I'll work on getting the speed up. But with required full speed tracks, you just end up being unable to make a jump and then when you finally do make it past that part you have no idea what to expect so I immediately crash (and watching the "GPS" does not work for me, I won't remember it unless I've driven it myself).
Similarly back when I used to play piano I would start out slow but once I began to internalize the movements I could get up some good speed. Not as fast as this guy though (the insanely fast bit is at the end of the video):
Note that a piano, because of the mechanical movement of the hammers, has some pretty large lag between keypress and sound.