About classical musicians not composing and all that,I have a contrary opinion:
I thought that improvising was creating something that doesn't exist,and on the fly.Isn't that called composing by another name?If one guy improvs and plays on his guitar,and another writes what they hear in their heads on a piece of paper(in note form),what's the difference?It's all creation!If you ask me,composition,improvising,these are just different perspectives of the same animal,really.
But then again,I guess it's a bit like raising the question of whether an actor who works from a script can do stand up comedy or mime,and vice versa?
Hmm.