Hmm ok, sure. But please bear in mind that I only watched through the whole show once and it's been several years, so if I'm remembering anything wrong that's probably why. And these are just my opinions, so I'm not saying everyone needs to agree or see it my way...
Here are my semi-coherent thoughts on how I felt Zuko's character was mishandled
In general I didn't like the pacing of atla. Things I thought should have been handled slow were rushed, and things that were focused on seemed to waste a lot of time... a lot of this was probably me looking for something different than what this show was, not because the show itself was bad. But I was often frustrated about what was given attention, and when, and what wasn't and why. There was a lot of contrived moments that seemed like the writers pulling strings rather than allowing the story to play itself out. It's hard to describe what I mean by this, so maybe this doesn't make sense.
But as for Zuko himself, I didn't think his transition was completely realistic, especially not without more moral support. But instead they made him into a woobie character to gain sympathy points. But I wanted more of the bad-assery he'd shown in earlier seasons. It seemed like they took away that and made him sucky to gain audience sympathy. But it just felt really unbalanced. Katara is literally the strongest waterbender, she doesn't even need more than like one day and is already beating the master guy (which i hated), Toph is literally basically the strongest earthbender, Sokka is at least a decent strategist, and Aang is the Avatar.... And Zuko kinda sucks at firebending. But I'll touch on this more later.
Aang and the gaang doing more to convince him would have tied him in more strongly to the others without the pointless and blatant "let's give each character an adventure episode with Zuko because it's what we have to do now" episodes. They wasted so much time, when they should have found a more natural way to do that. How about somewhat still proud Zuko actually talk with them and they learn more about each others lives? Then Zuko could grow and the Gaang could start seeing him as more human, and they could bond more naturally. It would have been a real test of Aang's views of the world and would have been a great way to build Aang's skill's in persuassion and peacemaking. Especially if Aang isn't always able to answer, or even struggled with some of the thing's zuko says. I would have liked to see more conversations/interactions between him and the Gaang to help him grow and to form bonds over that. Instead it's too abrupt. He gets humiliated a few times and pretty suddenly he has all the "right" views. And then begs them to accept him.
I wish the father wasn't such a cartoon villian (but then, it is a cartoon...). I'd have liked just a little more nuance and a little more struggle on Zuko's end emotionally and psychologically. Even as he decided that what the fire nation was doing was bad, in real life people will not immediately adopt the exact same ideology of the other side. Even kids with abusive parents still love their parents and will often try to protect them. His father's approval was so important to him for so long, that I don't buy him suddenly despising him like that. What if he'd tried to convince him instead? His moment of "you suck" to his dad just seemed like how a kid would write it. And since it's a kids show, I don't think it's a good idea to be teaching kids that seeing the difference between good and evil is so easy and obvious.
I wish he'd been given a little more to do after joining the gaang. This relates to what I said above about him sucking as a firebender, but he doesn't really do very much after changing sides. He was supposed to be Aang's teacher for firebending, but they didn't even let him do that. He and Aang had to both learn it from another source. This seems contrived and just irritated me. You mean to tell me all firebenders don't even know their own craft and have been doing it wrong for ages? You mean all firebenders are perpetually angry all the time? How did Zuko firebend before he got banished? He didn't seem angry back then. This was just stupid and took away whatever role Zuko had.
But the thing that I absolutely cannot forgive the show for, the thing that made me so mad, was the one thing i was waiting for, the one moment i thought they'd finally give him to let him shine was his battle with Azula. And yet they couldn't even let him have that, instead Katara had to come in and rescue him. They built up this epic rivalry and feud between them, they have Zuko learn a totally different way to firebend (ok, fine, whatever), show him how to lightning bend, talk about how much less talented he is and how he's always been overlooked compared with his sister... and he can't even beat his sister without a random third party stepping in to defeat her and save him. This would be comparable to Sakura coming into Sasuke and Itachi's fight and defeating Itachi in the end. Just no. Katara just had so much less stakes in this fight than Zuko. We already knew Katara is the best at everything, so her defeating Azula wasn't a big deal. The writers should have given her something else to do and Azula should have been defeated by Zuko. It would have shown why his new way of firebending was better and how he was a stronger person than her because he had to learn to do things the hard way. I just hated that Katara defeated Azula so much.
I think maybe if Katara and Zuko were at least romantically attracted to one another it would have been slightly more understandable from a character perspective and have tied in better... but the writers wasted so much time making sure everyone knew they'd never end up together and couldn't let go of her and Aang together, which I personally never liked. I think this is why they kept Zuko apart from the Gaang for so long and had all his character development take place separated from them. And why his interactions with them seemed so off and stilted. I think the writers were letting too much of their own preferences dictate how they wrote the story to the point that it was really noticeable and it really irritated me.
Anyways, these are just my thoughts. In the end it's a pretty lighthearted kids show and i probably shouldn't have expected more. If I'd have kept my expectations lower I probably wouldn't have felt so let down and irritated by what the show actually was, rather than what I wanted. I really like character's struggling on the edge of good and bad, so all that being said, Zuko is still probably my favorite character of the show. But that's why i found his development so frustrating and annoying. In the end I just didn't like the show as much as everyone else seemed to.