I can see where you're coming from with this. When I saw the end, I read Azula losing her sanity as sort of a snowball effect. The danger was always there for it to happen, Mai and Ty Lee betraying her really got the ball rolling, and it quickly picked up speed. I think she would have been fine with power (as was shown when she took over Ba Sing Se), had she not been unhinged.

But still, I read it as the betrayal unhinged her so badly, and she had absolutely no time to recover from it.

On a side note, I think I fell in love with Azula as a character in "The Beach," when for a brief moment you see her facade fall when she says her mother thought she was a monster. It was in that moment that really added a lot of depth to Azula, I think.

It's interesting to think about!

Lastly, I'm very glad that Zuko's scar wasn't healed, and yeah, it would be a terrible reminder about how incredibly messed up his family is.