The true question: To crit or not to crit?
I've been playing for several years now, and every now and then a certain question has popped up since they had decided to remove "Dodge" as a status: Should we keep crit in the game or not? Are the benefits of crit even weighting up the problems it causes? And is it actually a mechanic we want in the game? RNG usually is not really popular in competitive games. That's not really a new thing either. Early versions of chess were actually played with dice... until someone said: "Fuck it, I want this to be a true battle of minds without any luck or misfortune interfering!" (also if we leave the dice away it no longer counts as gambling, giving us less trouble with the medival church) - a true competition, so to speak. And that's also something LoL is trying to strive for, trying to be an Esports "for generations to come". (At least that's how a red worded it some weeks back).
In the most recent ADC-Update there has been an attempt to make crit more bound to the AD-Class. Which was ironically unecessary, since most of them were building 2-3 crit items anyways while also being the most dominant role the game revolved around since season 2 (or maybe even earlyer, but I only started S2.) I cannot remember a single game when an ADC did not buy 
- with the exception of an occasional 
abusing whatever item was broken on him right now.
On top of that, the entire "we need to statbind the class to crit" argument was entirely unnecessary either: ADC's were already getting a stat neither mages or tanks ever bothered to look at, apart from a few exceptions: Attack Speed. Making some abilities have AS-scalings wouldn't be too weird. Lucians ult has it for example and it really feels natural. Like, the more speed, the faster the shooting, makes total sense.
However, the main problems lie elsewhere:
1.) Crit brings too much powercreep into the game. Why do melee carrys need to 2-shot adcs? So they are not 3-Shot by the carry. Why do need assassins damage values that turn them into mobile burst mages? Because otherwise they couldn't do their job properly. Sure, it might seem unfair when that Talon, Zed or LB just deletes you from the game - but... there is just no alternative. Either they delete or get deleted.
Over the course of years the meta has constantly revolved around "how to stomp that adc as hard as possible". Season 2 Mage Meta was based on the fact that burst mages could delete carries before they could shoot for 2 seconds. Season 3-4 Assassin meta was caused by the same. The tank meta finally showed a peak when defensive itemisation outweighted the basic ad/crit one, but despite many players found this meta to be quite pleasant, adcs had the short stick on it. Right now we have over-buffed a certain group of adcs (with a few exeptions, such as Varus) who now run rampage on multiple roles, leading to assassins become more popular again, but this time in combination with some weird tank items.
As long as the adc role is build around the high damage output due to crit, I doubt there is a way to find a meta that somehow pleases everyone. Or even better: the ideal meta where everything is somewhat viable. Also, I think Yasuo would be a lot less frustating without the crit passive (just let him scale with AS to prevent him go full-tank.). This also applies to many assassins, who actually could be tuned towards assassination instea dof "murder everything that is out of position, 100-0".
2.) Crit leads to bad champion design. As long as crit is viable, the basic attack of a champion is more important than the abilities - otherwise crit would not be viable.
But without abilities, a champion is nothing more than a gloryfied minion plus a few gimmics. Luckily we have seen some innovation with 
and 
considering unique attack mechanics and reloading (an aspect that should be defining for marksmen that use bullets). If the basic-attack is already that unique, the rest of the kit can be gimmics and tools.
Also, crit not existing would allow us to make the abilities of ADCs stronger, making the champions feel more distinctive and unique apart from little variations of the "right click until enemy dies". Abilities ARE the defining point of a champion after all - and that includes a reload-mechanic.
Btw: Candidates for a reload mechanic: 
, candidates for unique attack patterns: 
. Everyone else has some thematic excuse. Lucian doen't use physical bullets for instance. Going through with this would leave most adcs untouched actually - just saying this before everyone in the comments starts raging again.
3.) The RNG nature of it. It seems annoying to bring this up yet again, but there is a difference in winning a contest with luck or with skill. Luck either causes you to feel like you didn't deserve it, or that the game itself is messing with you. You know that feeling when the enemy adc just gets 3 crits in a row despite only having bought an infinity edge? Super lucky for them, but to you it just feels like the game is inentionally trying to screw you over - not exactly a feeling that should occurr in a competitive game. If I die I want that to be because of my own mistakes, not because of luck and misfortune.
4.) Crit is limiting item choices. Just compare AD and AP and Tank itemisation. Despite AD being stronger, it truly lacks variation, especially when it comes to item effects. That's mostly because when an adc has to devote 3 slots to crit items, a 4th one to boots, 1 slot for a def item, there is maybe ONE slot left for an variable item. And now compare that to the slots mages/assassins have to dedicate mostly: Boots, Deathcap, Mana (if needed). That makes 2,5 slots, as compared to 4-5.
Also, there is one thing I always read in such discussions: "But without crit, adcs would totally be the best at tower-wrecking - even worse than now". That's not a matter of crit existing tho, that's an adjustment that can be made to towers, defining how much damage they recieve from ranged basic attacks. Apart from that I can't really think of a single argument that actually speaks FOR crit being in the game.
But the more I think about, the more I find reasons to how removing it could help this game a lot.
+ situational item.