Perhaps there is a question of how a song is learnt. If you’ve read it to play it, then it’s more familiar to read from a page. If you’ve learnt it by ear then you hands are one step ahead of you.
if you’re unfamiliar with what you’re playing at a gig, then you’re either incompetent( if it’s your regular set) or a quality musician capable with dealing with the unknown. The latter should of course be allowed any tools to make the performance the best it can.
safe.