This is admittedly going to be a little "off the top of my head" but I have a suggestion that could be implemented to replace crit chance.
DISCLAIMER: The reason I believe that Riot needs to remove crit chance as a mechanic is due to the shift in how League is played. League used to be purely a game, but recently it has become very competitive and is now more of an ESport than a video game played by casual players.
The change I propose is to implement a mechanic called "Precision".
Precision increases basic attack damage by a percentage equal to the old crit chance (50% Crit from a Phantom Dancer would give 50% increased basic attack damage), this removes the RNG element but still allows for pure dps builds to be stronger than full AD builds in terms of raw damage per second.
Infinity Edge would be reworked to increase your precision by 50% (If my math is correct) as that is the amount of additional damage on top of the extra that a crit would already grant you.
All abilities that scaled on crit would now scale with precision, allowing abilities like Alpha Strike to be itemized for, but removing the chance of 3 lucky crits getting Yi a pentakill.
So, what are your thoughts, Summoners?
Anything I've missed that would prevent this new mechanic from working? Or is it just a bad idea in general? I'd love to hear from you all :)