I honestly think its the whole "merchandise" idea - Easy one-trick champions like Yasuo and Yi sell a lot of merch and are popular among the mainstream crowd. I mean, they aren't hard to use so its not a surprise people enjoy getting many easy wins off of them.
My issue is what a plat told me years ago about "making mistakes" - if someone makes a mistake in lane, you punish them. The problem is, how do you punish Yasuo? His E is ready half a second after cast, just a cooldown on which target he can hit. His Q goes around 1.3 seconds at max rank and something like 5 seconds at level 1. With these URF like skills, no matter what he does he can just cast it again quickly, so there's NO punishment - if he misses he just recasts and recasts and there's literally nothing you can do. The Phantom Dancer change, while a good start, gives yet another god damned shield he doesn't need.
It is one thing to have no mana, but to have nearly non-existent cooldowns as well? That's the problem. How do you fight early game against Yasuo when he can push you to your turret and take 60% of your health in two hits? Cast all you want, he'll heal for more than you hit him with. I've also used Yasuo, gotten S's like candy, and soloed rift herald with 3% lifesteal - it is INSANE how easy it really is. I took out a Malphite with four items when I had PD, IE, and Doran's Blade. Too much damage, crit, lifesteal (his Q is treated as single target even when the whirlwind hits multiple people) and no punishment if he spams his abilities.
You want to balance him without making him weak? His E has a fixed 3 second cooldown, unless it kills a unit in which case it refreshes. His Q heals for 33% instead of 100% since it can hit multiple targets. W starts at 2 seconds at rank 1, 4 seconds at rank 5. This isn't really complex.
Yi just needs his ultimate changed significantly so it can't stack up to 35 seconds from kills/assists and refund his cooldowns. No assassin (yes, that's his listed role in LOL's universe page) should have true damage and immunity to attack AND movement speed slows and heal for hundreds of health with a meditate while halving most damage. How do you fix it? E true damage is removed, if he takes damage in his W it stops and goes on cooldown (no more reducing damage) and his ult is limited to no more than 14 seconds (one ult cast and one refresh from kill/assist) with attack speed able to be slowed but not movement speed, OR the other way around.
No reason these two should be ruining games for the last 6 years without significant nerfs unless its based off bias and that's why nobody who created a champion should be allowed to balance them!