You apparently don't realize how few champion design/rework teams Riot has compared to the resources they have available. They have several new champion design teams, 2 VGU (visual and gameplay update, like the new Warwick rework) teams, the champion roster team (think the assassin updates), and the balance team. I know that they were originally planning on doing divers for midseason and Aatrox was going to be on that update, but now they've changed their mind to tanks and have confirmed that he will be getting the size update he would've gotten in the diver update before the tank update goes live.
Kalista and Azir, on the other hand, are the result of some of the last massively overloaded kits with insane skill floors that Riot put out. I'm gonna guess Aurelion Sol falls into this category, too. Champions with insanely high skill gaps, but if you can figure them out, they're busted. With all of them, something is gonna have to give. Kalista will be between Rend being Smite, but better, her insane kiting, and her ability to save her support from any bad situation. Azir will be between his DPS from long range and his Shurima Shuffle (personally, I would get rid of the Shuffle and ramp him up in ranged DPS). I'm not sure what Sol would have to pick and choose between for him to be able to exist and be strong, yet healthy at all levels of play.
Nidalee was the queen of the jungle for the entire last season, no matter how they nerfed her, but got kinda destroyed by the jungle updates and is in a state where it's incredibly frightening to put power back into her kit for the same reason as Kalista and Azir. If they put some power back in, it could either do nothing or make her busted again and it's near impossible to find that sweet spot.
As for the rest of them, I for the most part can't find much wrong with them. Morde and Shen are the 2 biggest problems, but I don't know how they could change them. Riot has said that they aren't happy with Shen's spirit blade mechanic, and it's probably going to be reworked in the future. Morde on the other hand needs a full VGU to fix the fuckery they put on him, and I don't know how that's going to work. Rek'Sai, Kog'Maw, Kindred, Malzahar, and Skarner are pretty fine right now, I feel. Skarner might be able to use a passive different from the crystals just because they kinda force him into the jungle, but they're still kinda cool and work decently well in my opinion. Otherwise, I feel like he's fine.