I memorized most of the technical aspects of every song I played, and the sheet music was more of a guide to remind me of the nuance, context, etc… No one (good) is relying entirely on the sheet music. It’s like GPS: I’m still relying on my own knowledge and skill along the way and the GPS is just a guide.
Gigs are another thing. There’s a different sort of skill in playing entirely from the sheet music. Especially if it’s uncommon/unknown music. You usually have a handful of practices before a performance at most, and you drop some nuance to ensure you play exactly what’s written on the page.
It’s like DDR. You shouldn’t have to look at each note to play it. You scan lines, get the gist, recognize the patterns, and just let them come out of your hands and mouth while you’re scanning ahead to the next line.
I never even consciously noticed that I was turning pages once I was good. It just happened.