The problem is that it adds far too much variance for not the best reasons.
Let's contextualize this with a good example of variance; which side of the map you're on. Both sides of the map have different geography, buff placements, and epic monster preference. Furthermore, which side of the map you're on is mostly random. Despite being random, nobody "loses" for being on one side or the other. Instead it presents a situation for the player to work out: How do you take advantage of what side you get? Does it affect your early clear pattern, how you prioritize ganks or epic monsters and so on and so forth.
Critical Strike Chance does basically the opposite of everything described above.
Don't Crit? Deal some damage. Crit? Deal a lot of damage. Big difference from before is one player wins and one player loses in this situation. It also doesn't affect decision making in a strategic way for the most part; most champions building Critical Strike chance were going to auto attack anyway. In this effect, Critical Strike chance is just an extra RNG flare onto an already intended action. There's little depth in Critical Strike chance in this matter, and it's mostly a big red flag for bad RNG design.
Evaluate the Critical Strike chance systems of other games and consider what they're there for. What they're really there for. You'll find they're actually well designed forms of RNG (old Role Playing Games), mechanics with purpose (Pokemon's Critical Strike Chance), or actually badly placed (competitive strategy games).