......never performs, plays only a small number of pieces apart from his own, and who does little else but obsessively record many hundreds of hours of improvisation. The need and psychology are probably very different.
I think that when pianists improvise, they do so to their strengths and avoid doing stuff that's technically challenging for them. I certainly noticed that when I improvise, I never ever played double thirds, or trills involving the 4th & 5th fingers while playing a tune with the other fingers, because I'm rubbish at them. Art Tatum played a lot (I mean a lot) of fast RH runs in his arrangements and improvisations, because he was brilliant at them.
But classical pianists don't have this luxury and have to be able to do everything composers ask for, whether it involves getting the fingers and hands tangled up with each other (Ravel), or very fast thirds and sixths (Chopin et al), fast leaps all over the keyboard (Prokofiev), fast octaves and chords and repeated notes (almost everyone from Chopin, Liszt and Brahms onwards....). So, we have to warm up for every eventuality. Or just avoid some composers like the plague......