I'm not terribly thrilled with the idea of music as a competition, either. If you can play a piece of music with skill and expression, everyone wins.

But... if my DD were intrinsically motivated by that sort of thing, and she practiced with more enthusiasm and pushed her abilities as a result... why not?

In your place, I would look at bringing my DD to a competition as an observer. Let her see what the competition experience is like, what she would be up against, etc. And then I'd let her make the call. If it's something she wants to be a part of next go round, fine. If not, that's perfectly fine, too.