Good point, it is exactly the added pressure that performers experience when they play on stage... And that is precisely why some artists play/sing on stage to recordings of themselves in "live" performances at venues which allow it.
Wasn’t it the case of Glenn Gould who stopped doing live performances because he was not happy with the possible quality he could reach with them?
Also I believe he was hold back by the sound quality, not by his insufficient ability to play… Was he the first “victim” of the tech-trap?