I found the Netflix version of the show (supposedly they messed it up somehow?) to be really cute, and I pretty much agree with what you've said. She's not TOTALLY incompetent as it goes but sort of still is.>>2990752
I think we're only supposed to hate her because she's a smug entitled jerk, and the teachers auto-love her by reputation while shitting on the new student. She looks down on Akko for the most part
But it reminds me of Kill La Kill where the main character is a variation on the "chosen one" trope, but there's a secondary character who is as good as or better than the protagonist... except Diana and Satsuki got that good because they worked for it - privilege can only go so far in making you smart or strong.
Ryuuko and Akko are tenacious, but most of the power they have in the story is because of the chosen-one thing. Ryuuko is [however the hell you do spoilers right], and Akko found Mr. Special Wand in the first episode and is then heavily supported by Glasses Sensei.>>2989937
Maybe they are saying each other's name?