I Am Completely Serious

I have poor taste, so I really liked early Azula. I just enjoy insanely over-the-top powerful all-knowing two-dimensional villains like early!Azula - when they're snarky. (I do not enjoy, for instance the Bleach Jerk, Toguro from YuYu Hakusho, or the guy from Flame of Recca.) So for me, the issue with her characterization isn't that she's shallow and crazy-overpowered, because this pleases my inner five-year-old, but that she's not consistent about it.

That weirdness about Ty Lee and Mai's motives is definitely the sort of thing that bugs me. Part of why I particularly object to her ending is that you can totally make these sorts of omnipotent villains screw themselves over in ways that make sense in their own context. (Given that it is impossible for them to make sense within the context of reality!) Magus from Chrono Trigger is my favorite example of this. Both before he messes up and after, I think his behavior is pretty consistent within its own absurd parameters. Professor Nova from Battle Angel Alita goes through self-destruct and rebuilding cycles something like six times, but he's always the same shallow, ridiculous character.

Whereas the laws governing Azula's behavior aren't consistent - socially incompetent party-goer Azula is not the same character as evil childhood flashback Azula, who is definitely not the same character as Crazula. Her losing her grip is not only part of a sexist pattern, it doesn't even make sense within the story.