When it comes down to it, crit really just needs to be removed.
It's difficult to think of an issue in game balance not tied to crit. But, anyway, I'll list the reasons why crit is horrible for the game and needs to be removed.
1: It's random. This isn't a luck based game. If you want a shot at cheating destiny try a casino.
2: It destroys AD itemization singlehandedly. Crit, horrible stat that it is, is basically useless on every champion who isn't a ranged AD and/or Yasuo. This is a problem because every high end damage focused AD item relies heavily on the stat. Two and two together and the rest of the AD cast, especially bruisers, end up having especially terrible item choices, most of which feel horrible to use. If you deleted crit and replaced it with an AD deathcap, you'd first need to rebalance a few champions and rework some champions who are especially reliant on crit. I can count said champions on one hand. But more than that, itemization for a large swath of the roster would be vastly improved.
3: It overpowers ranged AD's half to hell. If you're honest in the least, you admit that ranged AD's are exceptionally overpowered. And kind of have been forever. This is basically because they're the only ones who can actually abuse crit for everything that it is. If you removed crit, you could buff these guys early. Actually highlight their differences instead of focusing on the one thing that makes them all identical. Make them less unhealthy for the game as a whole. And make them optional. Which would be the best part.
4: It's why bruisers need to be intentionally overpowered to be worth playing. Alongside red buff. Kind of. Problem with melee AD champions is that they need to stay alive long enough to do something in a fight. And the problem with that is that ranged AD's kill everything in about a half a second unless it builds full tank, in which case you've got maybe three. Without ranged AD's being heinously overpowered, brusiers wouldn't need to be either.
And then you think, what does crit actually add to the game? Answer is absolutely nothing. Some people would say "Oh, it's necessary because without it nobody would be able to kill bruisers", but that's a flawed line of thought because if crit didn't exist bruisers wouldn't need to be made as ridiculous as they are. And....
Actually, that's the only half sane argument I've ever heard being made on crit's behalf.
So, Riot. Here's the thing. Deleting crit would be something that's a little bit difficult. It would take a while, and in the meantime there's a chance that the game would be somewhat imbalanced. So I'm not saying that we need to drop everything and delete crit instantly. But you need to start making incremental adjustments removing the stat slowly overtime, until such a point where you can get rid of the last of it between seasons. It's necessary for game health. Also, you should delete Teemo.
Peace out.