Certainly; there's always room for another Azula fan

Azula always used her brains and laid things out. She thought ahead so much, none of the other characters had enough time to react.

Katara always seemed to just being pulling things out of her arse. But when Azula went insane, that was switched around. Azula was no longer thinking ahead, she was just making things up as she went along, so Katara had more time to think.

Doesn't make Azula less awesome, though. Crazula was still win.

In the finale, Azula's awareness of her surroundings was in shambles. Back in "The Chase", Azula could take one look at her surroundings and take in everything signifigant and figure out it's meaning in the space of a few seconds. In the finale, she didn't even notice that she was standing on top of a drain of water with a waterbender a few feet away. In any case, something I found very suspect about that scene was the fact that Katara was right in front of Azula, and yet Azula did not attack, instead walking towards her over the drain. If Azula had had her sanity, she would have blasted Katara then and there and the fight would have been over.

As for CoD, it is true that that was a low point for Azula, but no more so than it was a low point for Aang several seconds later when Azula blasted him across the room with her first shot. At the start of the CoD fight, Azula easily blocked a far larger waterbending attack than the one Katara got her with in the part you like to bring up. Sometimes shots get through; fights are like that.

Personally, this is my favorite part of that fight:

Katara can be gotten out too.

To adress your other remarks, we have no idea how quickly Azula achieved her Firebending skills, but we do know that she was already a brilliant Firebender at the age of 7, at which point Katara hadn't even discovered she could bend (as far as we know).

In addition to her incredible bending, Azula has also found time to become an incredible acrobat and martial arts combatant, and has implied knowledge of shruiken fighting too. Katara has nothing on Azula's tactical genius, manipulation, brilliant lies, general awareness, or charisma. And is if that wasn't enough, Azula is also a history freak who has apparently memorized several textbooks by heart. Beat that Katara.

In the final analysis, Azula's slide into insanity was the ultimate deus ex machina; necessary if her opponents were going to ever stand a chance.

We should have a new hierachy. Forget the whole president, vice president, etc thing that the other clubs have - we need something better, something more to Azula's tastes. I propose a Fire Nation theme. I'll be the Phoenix King, you can be the Firelord. The honorary members can become the Royal family, and so on.

Considering that this is only our second day, we're doing pretty good. Also noteworthy is that we're doinf far better than the other clubs, none of whom have thus far managed to exceed 10 or so members.

As time goes on, we will pick up more people. With Azula, it is inevitable.

You mean they already weren't?

Of course they can, and will be, provided that I become a candidate for Phoenix King in your club (I noticed the title and liked the look of it).