Yasuo is balanced. He's tough to play, tough to play against. He's got lots of resources. He's a prettyboy samurai, high profile VA, good lines, some weeaboo Nippon thrown in there. He's got a huge katana, he has poke, he gets great damage early off far less gold than others. He can contribute to teamfights while behind and end them abruptly while ahead. He enjoys a solid solo experience but absolutely gobbles up synergy.
Now assume three people played a champion, do you think you'd get a lot? Probably not. But if hundreds of thousands play him and want to play him and play against him? All of a sudden you have this funny number bias. Just because he's popular, things seem so skewed. But realistically, he's not really that different than others. And if it wasn't him?
Just a smattering of champions who have historically been as popular as Yasuo for hate-on. If he weren't popular enough to garner this kind of attention (
) for any reason, he wouldn't get picks; he wouldn't get bans; then, nobody would talk about his balance, whether it existed or not.
Ahri's been the exact same champion design for a long time. As the meta evolves, she seems to get a change one season, which reverts, then another, and a revert. They lastly added her Q MS. Anyway, people have always hated Ahri. Too strong, too fast, too bursty, too much CC for an assassin, you know the drill. Fact is, her design's been the exact same except maybe level order and rotation, since she stepped off the plate to my knowledge. And people have always hated her. That's because they see her a ton; Galio got reworked and now people see him, and now people hate him. Nobody barely talked about Galio before; not as destroyed as Morde was, and not as clunky as old Sion was, he was pretty much a 'yeah, he could use a touch' almost any time he came up. They modernized his kit to have mobility and hey-- look. People hate him now.
People don't like a lot of things. But if Riot starts balancing, deciding things, based on what does and doesn't hurt some peoples' feelings in lane, their champ design is going to go to absolute garbage. Nobody has to like Yasuo. They don't even have to admit that he's balanced. He just has to be; and as long as he's balanced, he can get perma-banned from 99 games of a 100 and it's still just fine. The essence of balance is, 'can it be beaten in a standard scenario?' Not, 'do people like this?'
If it were something like 15 or 20% of the cast that suffered like Yasuo? Sure. But it's a handful of champions, and most actual balance discussions end in people screaming and swearing about how much they don't like facing opponents who defeat them, because they won't DODGE THE GOD DAMN LUX Q IT'S LITERALLY A STRAIGHT LINE!