Kali and Azir are not 'popular', they were flavor of the month when prominent players decided to play them. Zed is still out of control with Duskblade and the current state of the midlane. Riot has been discussing completely reworking Kalista and Azir for almost a year now and when you look at recent hated champions you start to see a pattern.
Ekko (another champ people are polarized about) came out about a year ago. Since then, he has gotten a figurine, a hoodie, a t-shirt, 3 skins (one of them being from the highly coveted PROJECT line), and a plethora of screentime both in game and out of it. Compare that to his release buddies Rek'Sai and Tahm Kench. They were released before and after him and neither of them have anywhere near that amount of attention (no shirts, no figures, no hoodies, nothing).
Yasuo is just like Ekko, but over a longer period of time. He has a full Twisted Fate-style figure, lots of shirts, lots of merchandise, and has a kit so overloaded he's basically 5 champs in one. He and Ekko enjoy a high level of play due to their crazy mechanics, therefor they enjoy a higher level of marketability.
Remember how Kalista got completely destroyed after LCS and Azir wasn't far behind? That didn't happen to Yasuo or Ekko because they have a long-term devoted fanbase while Kali and Azir were just passing fancies. Any changes made to Ekko or Yas take AGES to actually come into play because Riot is so scared of stepping on one of their biggest money fountains but at the same time they're tying to control the monsters they've created.
I seem to recall Riven being given an Edge resource that would've made it easier to play around her and give her a bit more complexity, but Riven mains launched that idea into high orbit because they didn't want Riot touching their girl. The same idea applies. A few patches ago they didn't even nerf Yasuo himself, they nerfed Frozen Mallet, an item Yasuo players love to build. They literally danced around the actual problem and instead of curbing Gnar or Yas they slightly adjusted one of their niche items.