Katara is bullshit. She starts the show as a completely shit bender, by The Waterbending Master she's improved a little but Aang is obviously leagues above her and then suddenly by the end of season 1 she becomes a master waterbender much better than Aang because "Aang is too busy playing to learn" even though we've seen before that Aang can copy waterbending techs literally after seeing them used once.

Toph and Azula were both prodigies who spent their lives training in some of the best conditions, the strength they're introduced at is the strength they stay at. Zuko had a lot of growth but even in the beginning he was able to beat Zhao, he went from stronger than the average firebender thanks to years of Iroh training to near-master tier after a dragon power up and finally stabilizing his emotions but he still couldn't beat his sister after she had a mental break down. Meanwhile all Katara needed was a couple weeks of training from Pakku and suddenly she's Avatar-tier.