In real life, lots of things that happen in one piece wouldn't happen, including many of crow's badic abilities. I still try to figure out where the water is supposed to go when he uses his drying technique, since water displacement is a thing, and why water is croc's weakness in most cases but he's okay moving it with that ability, or how he can move several tons of sand, but water making it marginally heavier renders it impossible.
One piece mixes with real life the way cats mix with the empty vacuum of space. Pick any fictional series at random and you'll get one that is more believable. You can argue one piece operates well enough in its own bubble, but that's the only place it can operate.
On the other hand, most of what Azula pulled off was psychological warfare against indoctrinated servants. They were brainwashed into a might makes right mentality. In her brief stay there, she managed to infiltrate and subtly spread doubt among the only enforcement running the show there. Azula's breaking speech to Long Feng played on the Divine Right to Rule belief, something deeply engraved into the culture of any monarchal society. Their king was weak, so they had to settle with the effective advisor. But now that real royalty stepped into the picture, they have a chance of serving a true queen. And that's what Azula played on. It might have turned out otherwise if Long Feng had more spine to him, but in their exchange, he was the one asking the questions of Azula, trying to regain control he lost. When Azula said he already knew he lost, that's when he hesitated, and actually did lose.
Perhaps you can gawp in disbelief, but the human mind is not rational and is capable of making strange choices where politics is involved, as exemplified by our current president elect. Nothing about Azula's rise is based in fiction, it's all mind games, and you can't disprove that.
Furthermore, there's one other difference. Azula never planned anything, atleast not beyond a step or two. Infiltrate the earth kingdom, and proceed from there. Then they find out about the Dai li, so she adjusted to turn them instead. Then she learned of the Avatar coming, so she adjusted to that.
"Plans can break down. You cannot plan the future. Only presumptuous fools plan. The wise man steers."
