There are traditions about memorization, and they are completely illogical.
It is logical that members of an orchestra do not memorize. They simply could not get through the amount of music they are required to play with the tiny amount of rehearsal time they have if they were required to memorize. We also don't assume the audience is looking at them.
It is completely logical that performers in any staged play, such as opera and musicals, memorize. It would look very odd if Aida carried a score around the stage with her.
Everything else is tradition.
In recital singers and pianists (solo pianists, not accompanists) memorize. Violinists and clarinetists don't memorize.
Vocal soloists appearing in oratorios generally don't memorize.
The piano recital tradition started with Liszt who extemporized extensively, but was slavishly followed by people who never extemporize.
Toscanini, near-sighted and Italian, worried about la bella figura and memorized everything.
Would we expect Madonna to appear with sheet music? A classical musician venturing into pop must follow its traditions.
If you are the focus of attention, the audience wants to see your eyes.
The reason that counts most: before a singer performs any piece, he must live with it, study it and absorb it into his soul. It's extremely unlikely that this has happened and he still can't remember how it goes.