Well... I think the classical world is subtly different from the world of folk clubs. The composer usually has very definite instructions on the score as to tempo, dynamics, etc., the conductor of an orchestra will also have definite ideas on interpretation, and - on the whole - classical pieces are far more complex than folk stuff. I've played (viola) in an orchestra and I can tell you that, by the end of rehearsals, the score was pretty much memorised. During the actual performance, we kept a close watch on the conductor for the overall cohesion of the piece.

As it happens, many classical soloists these days play their pieces by heart - i.e. not with the music in front of them. I would say that this is because, through constant hours of intense practice, they've got the score in their heads.