It's always hilarious to me when I see/hear someone calling Azula anything along the lines of "power-hungry despot".
Hungry for power? More like hungry for family/relationship harmony and rules.
If anything, she gives power away to others!
She helped Zuko get back the throne and (conditional) fatherly appreciation that he so desired, with her only request being that he side with her and their nation (that's not asking for very much, from her POV, mind you)!
She gave Mai a higher position than even her noble parents had and a chance to become a Fire Royal Consort through marriage to her long-time crush, Azula's brother, Prince Zuko!
She (albeit after first forcefully taking her away from her preferred surroundings) gave Ty Lee another, more exciting way (based on how much fun we see Ty Lee having) to feel different/special and like "her own person"!
She never used more force than was necessary when fighting her adversaries and only went "too far" when the situation seemed to call for it due to the risk to her person if she did nothing! (Which may have been a soul-destroying choice for everyone that was there [except Zuko]. Even Azula is implied to have felt like a monster for killing Aang, during that conversation they had on Ember Island!) A 14 year old felt forced to kill, people! That affects the one doing it, too!
Why does next to no one ever ask what Aang was even planning on doing once in the avatar state while they were in the catacombs? Especially from the POV if one of his enemies? Play hopscotch and do super gymnastics? Doubt it!
Now, please correct me if I'm wrong but, wouldn't a despot be preoccupied with looking for ways to change the surrounding cultures that they come into contact with? Instead, after she leaves Ba Sing Se, for example, she keeps it exactly as she found it; with the only change being the new Earth Kingdom-originated ruler she places in charge. The people of the EK didn't have anything change for them for better or worse, as far as I can recall.
Yes, we do see her trying to break through the wall of Ba Sing Se with that more advanced technology and she is imperialistic (which is something wrong in itself and which can be very brutal). But that's not automatically the same as being a dictator or snatching up bits of power from others in any way she can. And in the end she conquered it by instead using the true, least offensive (in multiple ways) means possible.
As for that period just before the final agni kai we see in show, where she was going to be crowned? She was granted that title by the current Fire Lord aka her father, after her back-on-the-clock brother defected (so willingly left).
take (a position of power or importance) illegally or by force.
"Richard usurped the throne"
Based on that dictionary definition, how can she be usurping Zuko's position if, again, the FL himself is giving it to her and if Zuko gave it up? She's literally getting it "legally" (the FL is the law) and without using any force!
Now of course there's a rabbit hole argument that some may try and use by saying that because Ozai himself took his brother's throne without Iroh's consent (was it without his consent? Iroh seems to never be in a rush to be FL), that Azula getting the throne is therefore usurpation.
Ummm, I hate to nip that point in the bud so soon but, Zuko is Ozai's son, not Iroh's. That means that (assuming the child of the by-birth king/queen is the only one that should gain the throne next if the king/queen is unable or unwilling) based on that logic, neither teenager should be allowed to sit on the throne.
Kinda hard to usurp a title from someone who "legally" shouldn't have it either, right?
Oh Iroh, if only you'd just done your damn job.
All that being said, literally all this girl was doing is finding ways to handle her job and fulfill the tasks of it that she's been given at such an inappropriate age, while amassing the least amount of damage possible. And along the way she tried to extend a hand to her family and friends too, almost as a sort of "sorry for the inconveniences/thank you for your cooperation and loyalty".
(She may have even learned some things about herself and others along the way—or could have, if she had been allowed just one more minute of screen time and the writing choice of change that the other Fire Nation kids got.)
Yet somehow many people come away from this show with the idea that she's trying to purposely take control of or harm as many people as possible in every way possible without any care at all for others' wants.
I know at least two characters that that partly or fully applies to, and neither of them are Azula.