Honestly, I like crits as a mechanic.
This may not be a popular opinion, but I don't think that crits should be removed, because they are one of things that separate ADCs from AD casters, which do not have crit and attack speed, but compensate that by focusing on their abilities to do damage.
In addition, crit is necessary to allow many ADCs to muscle their way past tanks. An auto-attack that is not backed by crits or on-hit effects is not going to do a lot of damage, even if you have a lot of AD. Have you ever tried to build an ADC without crits? There are some ADCs that indeed work well with a build that has little to no crit chance, such as 
but most of them have other ways to compensate. Kalista has her Rend, Vayne and Kog'Maw have powerful on-hit effects, while Kennen is not really meant to do a lot of damage late game, and he has on-hit hard CC.
But for example, a 
that does not have crit chance will do laughable damage at best, and will be outtraded by any competent ADC and by many other champions.
Also, as much as I hate 
, if crits didn't existed he would have to be reworked or else he would be completely useless as a champion
I think that the main problem with crits lie in 2 things:
-
Their random nature. You can have 70% crit chance against an enemy that has only 10% chance to crit. Statistically, you have way more chance to crit, but there is still a small chance that you will never crit and the enemy will always crit. This can be extremely frustrating when it happens. Also, imagine an
that has a complete Trinity Force (as it is now). You are almost outtrading her, but suddenly, she crits, and wins the trade because of that. This is so frustrating when it happens, that I think this is the reason why many players want crit to be gone. -
The way they interact with some champions and their kits. For example,
and . Jinx can have AoE crits, while Yasuo has doubled crit chance. There is also 
, which has the potential to have an high crit chance by early game, and with this, he can lvl1-2 cheese many champions, and potentially win lanes that he shouldn't win otherwise, with this way.
These are mechanics that interact with crits and make them be way more powerful than they should be. Crit is balanced, for example, in a champion like 
. She is a powerful ADC, but she doesn't really have any steroids or abilities that can interact with crits, therefore crit is way more balanced on her than on Jinx, for example.
I still think that crit should be kept, but reworked. I must admit that I don't have ideas to make crit less random and still balanced, but thinking better, maybe the reason why Riot added crit on many items, and is allowing ADCs to have 70% to 100% crit by late game, is because they are lowering the overall AD from ADC items to compensate. They will have less AD and therefore their crits will not do as much damage as now. And to compensate, they are allowing ADCs to crit more. This can potentially allow Riot to balance crit in a better way, because crits will be less random, as ADCs will crit more times.
As for the interaction of crits and abilities, it is a problem that I think Riot should try to solve in other ways, for example: Make Jinx do 10% less damage when she is using Fishbones.
As for Yasuo: Now that it is possible to get a lot of crit, maybe Yasuo can finally have that double crit passive removed. This can even allow him to have his crits do damage as normal, without the reduction that he currently has due to the double crit chance. He may become overpowered in other ways, though, but Riot can finally balance him once they make the changes go to live.