I would guess that there would be a fair number of classically trained musicians who've just been programmed by their instructors to not play anything that isn't written down. I think the best case scenario is being able to read music and play by the notes but also to play by ear, and there are quite a number of folks who can do that. Wish I had learned to read music when I was younger and I suppose I could still do it, but the truth is I just don't feel like putting forth the effort at this point. I can work out guitar arrangements by ear but my son, who reads music and has taken numerous music theory classes, can work out in a few minutes what it might take me days to figure out.