Pretty much this.
No matter how much people say again and again that she had background development similar to Zuko it won't make it true.
Zuko had three books to develop as a character, started showing his tense relationship with his Nation as soon as episode 3, and went against his goal of capturing Aang by episode 7 to save Iroh.
Azula is introduced as the new big bad at the end of Book 1 and properly appears in episode 1 of book 2, which is also the episode that sets her immutable personality for the rest of the book: she is ruthless, cunning, fixed on dominance and obsessed with perfection. She never moves from these initial traits (and neither do Ty Lee or Mai for that matter, they stay the same as they start as through the whole book). When does she get to show anything beyond what is stablished in that episode? In episode 5 of book 3, where suddenly the writers try to give Azula, Mai and Ty lee depth because they need to justify what will happen later on.
When people say that crazy Azula came out of nowhere they aren't exaggerating, it fucking did come out of the blue because until that point she had been a perfect villain fixated on her objectives.