I fully believe that if the boards had their way, every champion would be the same.

Champions in the game have abilities and/or combos that allow them to fulfill strategic niches that other champions don't fill. Some examples of these are traps mobility polymorph etc. (i would list more but these are the only ones I am 100% sure on, no I won't argue with you about Irelia's niche because if you don't see that her Q defines her playstyle then I don't know what the fuck to tell you)

There is some amount of overlap between strategic niches, but riot's goal is to make every champion have a specific reason to be picked. You pick over or specifically for Polymorph's guarateed CC and the life-saving ultimate that Lulu provides. You pick for the early game lane bully power that her traps and range provides. You pick because she is the mobile bruiser (yeah other champions like Yasuo are also mobile, but they aren't as tanky as irelia, there is an important difference).

These signature abilities tend to be very powerful and that makes people very angry. I won't lie, Caitlyn's traps are annoying to deal with, Lulu polymorph can feel extremely cheap because it's basically impossible to screw up, and Irelia's mobility makes her disgustingly slippery. But that doesn't mean their """problematic""" abilities should be nerfed.

If you nerf the abilities that make a champion stick out from others, then they lose their strategic niche and they lose what makes them noticeably different from other champions. Instead you have to take power out of other parts of their kit to balance out their strong areas.