I don't think that's so much self fulfilling as much as a non negotiable prophecy that's just going to say the good guy is going to beat the bad guy.

Yup yup! That's exactly what it is hahaha, it's very boring indeed, but the author does it over and over.

I think at some point they were playing with the idea that both characters were inevitably doomed but

I don't think it's possible. There is no room for ambiguity, since it says "And the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not ..."

This always leads, in literature, to the villain's underestimation of the main character. The character, like a typical Mary Sue, will discover the ultimate weapon, and regardless of what it is, the villain will say "no, I'm more powerfulllllll!!!!" and attack anyway, even though the prophecy clearly says that there is room for underestimation, and boop, ded.

What would be interesting would be trying to discover what it is that Voldemort didn't know that Harry had. Was it "the power of friendship/love"? Dunno, but that seemed to be a theme in the novels.

My favorite instance is the Greek tragedy about Oedipus and it is just so well woven.

We read a lot about that at uni when we were learning literary criticism. It's a really interesting one. :) I've always loved analysing these tales of prophecies and time travel paradoxes.