Maybe that's the only way to awaken her. Kind of puts a test how much you can trust someone.
Kyoshiro: Kuu, let me stick this sword in your chest to see if you're an angel ...
Kuu: I don't know...
Kyoshiro: *smiles* It's okay.
Let's go. Together.
Kuu: *blushes* Sure!
Kyoshiro takes out his sword, plunges it into her chest,
and nothing happens....
Kyoshiro: *tears flowing* Kuu... I'm sorry. Setsuna was right. You're not an Absolute Angel.
Setsuna: *laughing maniacally in the background* Man, what an idiot! Oh, well now I have Kyoshiro all to myself again!
As Kuu, lays dying in the flower garden...
Kuu: My prince, this is the last time I can write to you. I was an idiot. I trusted this guy and now look at me. I should have went with Kaon.
But then again, those Absolute Angels are probably sucking the life out of the normal humans to fight. She can just suck him dry as payback.