Like...I don’t watch ATLA and think “wow, Katara is the best most well-written character ever, I wish every character was this well written, this sure raised the bar” but...like I’ve run into approximately 50 million posts talking about how wonderful Zuko is and nearly as many praising Iroh and none of them have been framed as a refutation of people who hate him. It’s...weird.
And I also don’t watch ATLA and think “wow, Katara is a uniquely badly written character” either, I think the quality of her character (character as in, she is a fictional character, not character as in moral fortitude) is pretty consistent with other characters on the show. She’s complex, and flawed, and an awesome bender, and relateable, and all that. She’s sometimes righteous and sometimes petty. That’s exactly where she should be.
I haven’t done a rigorous analysis, but I’m guessing her strength:flaws ratio is pretty comparable to Aang’s or Toph’s or Sokka’s. Or Zuko’s or Iroh’s. Maybe she doesn’t have as much character growth as some of the other characters? But she does have some; for instance, her turning back from vengeance in the Southern Raiders episode is growth; her being willing to pull a con with Toph in that one episode is a sort of character growth (don’t ask me in which direction), that thing where she’s upset at her dad for leaving them but also doesn’t want to admit she’s upset is brilliantly nuanced writing. She’s a good character.
Is she emotional? Yes -- real life people often are. Does she sometimes go a little off the deep end with her idealism? Sure, and that’s both realistic and endearing. Is she bossy? Yep, but hey someone has to make sure camp is set up every night and no one else is stepping into that role. That’s extremely realistic for a girl who lost her mom at a young age AND had her dad go off to war, so she had to step into a parent-like role while still a child.
And usually when she’s being one of those things, she’s right. She uses her feelings to connect to people -- she can bring Aang out of the Avatar state when no one else can, and presumably helps keep him emotionally stable the rest of the time too. The way she sometimes lets her idealism shine through at inopportune moments is exactly like when Zuko spoke out at that first war meeting, even though it wasn’t his place and it wasn’t sensible. She’s right when she gets mad at Toph for not doing her share of the work, right when she gets mad at Toph for pulling scams on Fire Nation citizens, and she’s also right to be mad at Sokka and Aang for standing off to the side and rather than either backing her up or backing Toph up.
She does engage in small lies a lot and I’m not sure that’s always right, but again, good characters are a mix of good qualities and personal flaws.