Ryze and Azir are the biggest mistakes Riot has ever made
Ryze - because he's been reworked about 52 times and the same common concept that riot refuses to let gonof is what breaks him: mana ratios. Mana items are easy to buy and give him ridiculous power spikes. Buying tear and catalyst shouldn't be a huge power spike. Ryze has literally never been balanced because of this. If you gave him AP ratios that weren't terrible and removed his mana ratios, you could turn him into a less frustrating champion to play against because he'd take time to scale, not buy flat mana, hit 6 and combo you repeatedly while vamping back and perma snaring you.
Azir: because there's no counterplay at all. Literally the only champion in the game that completely lacks counterplay and has an answer to everything you throw at him. He is worse than Lee Sin, Yasuo and Zed when it comes to having to play on his terms, he dictates every course of action. The only upside is he's one of the hardest champions to play, so most people suck on him. But if you master this champion; he is free wins. And he has too much power in his kit.
These opinions might be unpopular but all you have to do is look at competitive play to see how these two champions have always gone through pick/ban or trash tier phases and that's telling you their kits can never be balanced.
Even frustrating champions to face like Zed, Yasuo and Tahm have weaknesses. They're all melee for starters. Zed doesn't teamfight well, Yasuo can be easily focused (but knock up comps need to be deleted or made significantly weaker, that's my gripe with Yasuo) and tahm doesn't do much on his own. These champions carry games by being huge lane bullies and the best scaling champions in the game and that shouldn't be.
So Ryze is slated for yet another rework, can Azir be reworked as well?
