AI doesn't compete just compete with "the underlying works" though; it competes with all works, even works that weren't in its training set. So the type of "competition" you're describing is incidental, and not connected to the AI's use of any particular copyrighted work it was trained on.

I don't know whether that makes a difference under existing law, but I'd argue that it should.

I'd also argue copyright/fair use shouldn't even come into play, since AI models do not (typically) contain copies of the works they're trained on in the first place (except in cases of over fitting), but that's a completely separate issue.