Being able to fully memorize the part can come in handy, but I would say it's down to the repertoire. Certain repertoire (like chamber music or sonatas) has an etiquette where unless all players have memorized it, you should also use music.

Also it depends on the instrument and how it affects the player. I think pianists don't get affected as much because they're more stationary, but when violinists or cellists have a music stand that's blocking them from the audience, their focus tends to go towards the music stand.

I would say it's like giving a speech. It doesn't have to be fully memorize but one should have enough of it memorized to be able to focus on the musicality and meaning behind the notes.