I think these are all excellent points, and I think I agree with them, with one caveat: I don't care about how the ending of Azula's story was fumbled, because she was so badly written from the beginning that I was never even invested in her as a villain, much less as a person. She was way too overpowered, which I could have lived with if she hadn't also been written as omniscient, and she moved around the canvas in a way that was pretty much plot-dictated and completely independent of the physical laws that the protagonists were bound by. Azula could be anywhere in the world at any time; she knew everything there was to know, including things she shouldn't, that couldn't even be explained by strategy or insight, and her most consistent characterization was a cartoon psychopathy. The writers couldn't seem to decide whether her posse hung out with her out of fear (implied in the scene where she recruits Ty Lee, referenced in the scene where Mai betrays her), boredom (the recruiting scene with Mai), or genuine friendship and like-minded sociopathy, which is what you'd get if you just watched them on any given day. It was mind-boggling to go from a complex, competent-but-self-defeating villain like Zuko, whose motivations and actions always made sense, to Azula, who was as two-dimensional as they come. I've enjoyed plenty of villainous characters in my time, but I'm at as loss as to what there is to enjoy with her.

So I can't really get outraged about her lousy ending, although I acknowledge it as being part of a larger trend in the writing.