Korra was actually bad at pro-bending and air bending. She had to work hard to get good in those areas (at least, as hard as can be expected for subplots in a 13-episode season). As for character flaws (typically a sign of someone not being a Mary Sue), did we not watch the same Season 2 where she continually fucks up because of her recklessness? I mean, if you want to say Korra was not written well in Season 2 I'll agree - she was infuriating. Most of that was Relationship Korra, which is hopefully over now.
The Avatar state has never been earned, and that's a flaw going back to the original series. Aang only defeats the Fire Lord because out of sheer luck hitting his neck unlocks the Avatar state again. I thought Korra Book 2 was going to have the balls to get rid of the Avatar state forever, and it soooort of has, but not really. Hopefully from now on it won't be powerful enough to be a get-out-of-jail-free card.
Eh, I guess? For all intents and purposes, she really hasn't had to work that hard for the elements. Most Avatar's don't know they are the avatar until they are a young adult. Korra was able to bend as a child, therefore they put her into training much earlier. By the time she was a young adult, she pretty much knew all the elements besides Air.
And this was all before Book 1 started. SO while yeah, she had to struggle to learn that, Korra's story is
NOT about her struggle to master the elements. It's more so her inability to be the Avatar (as a unifying person). She herself is not unified, and is internally in turmoil. She struggles a lot with being at peace. That is ultimately what this show is about, and why there is so much focus on it. THAT'S fine...but not when she's constantly taking three steps back in her character growth. When her inner turmoil becomes toxic, and she becomes an insufferable person.
Aang's struggle to learn the elements was pushed by his
obligation to abandon his youth and innocence, and give himself to the world to stop Ozai. ATLA was structured in a way though, where each struggle to learn an element quickly, was impacted by the his time running out (and the struggles of him having to grow up in such a constraint).
If you ask me, Aang's story was infinitely more interesting.
His struggles were a lot more relatable. Korra...mostly just struggles with herself, and constantly fails at it. It's damn frustrating.