The point made by jdw -- that some music is so physically complex that you have to memorize
This was actually said by bennevis--but I don't mind getting credit!
No worries, mate - we'll share the credit (?)
But what hasn't been said so far is that if you choose to play from the music (whether or not you actually look at the score), you'll also need a page-turner. Accidentally turning two pages instead of one in the heat of performance can lead to catastrophe.....
BTW, has anyone seen the 2006 French film La Tourneuse de pages
where the page-turner wreaks havoc on the pianist, who became too reliant on her? Beware!
There's also a sort of 'inverse snobbery' (for want of a better term) going on among some pianist-composers where they play from the scores only when playing their own music, to show that they aren't improvising the music and that their music is properly composed, just like the Chopin or Beethoven that they play in the rest of their program, even though of course they know their music inside out. (Hint: Stephen Hough). Of course, the score could just be a few sqiggles or Egyptian hieroglyphics, just like Beethoven's score for a piano concerto he'd just composed and didn't bother to fill in the piano part properly before performing it, to the horror of his page-turner.....