"Would you go and see a play and the actors read from the script?"

Possibly yes. I think the term's something like a "staged reading".

Classical musicians usually play from music and get paid. Possibly the origin of folk musicians not using words and music lies in roots in pre-literate societies.

There are times when your mind goes blank, no matter how well prepared you are - I went through a phase many years ago when I couldn't remember choruses - so if I'm doing a singing gig I'll usually have the words with me just in case. When I played in a ceilidh band we never used music - just a tune list with keys, but for an RSCDC dance I'd always use music, as the custom there is for the dancers to stipulate the dances and hence the tunes.