There are some performers (singers more than instrumentalists) who will hold everything up while they insist on finding exactly the right piece of paper. (The larger the singer's folder, the more likely they are to do this). That is just plain rude. If someone can perform with a bit of paper without it interrupting the flow, fine.

It is also a bit irritating if people can only do the version of the song or tune they've got on paper in front of them, when there may be good reason to do a different one, which they should be able to pick up on the fly but won't.