The thing that bugs me most about Irelia is not here damage, durability, stickiness, or disruption.

It is the fact that you literally cannot shut her down. Her Q reset spam on minions is one of the most brainless things in the world, giving her the ability to clear waves incredibly quickly with just a sheen. Once she gets tiamat (she doesn't really even need it truthfully), she can legitimately clear an entire wave in mere seconds, rotate to another lane, do it again and again. This means that any lead you build in lane through CS and experience really will not stick as long as the Irelia is willing to power-farm for a few minutes. It isn't Gangplank levels of bad, but it is close. It at least took Gangplank time and items to scale up and clear waves, Irelia does it with one item.

I compare this to facing Tryndamere in lane. The difference is, Tryndamere stays in the same lane and does it indefinitely, so you are left feeling like you have to baby-sit him or he will simply outscale you. That is frustrating, but if you are ahead and continue to shove against him, you can keep a lead. Irelia just goes to another wave and clears it and comes back before you ever have an opportunity to attempt to shut her down. You are left feeling really similar to how you feel about Tryndamere: you have to baby-sit her because any lead you have quickly dissipates because of her absurd ability to insta-gib waves (whereas you really have to just baby-sit tryndamere to shut down his split-push). The difference is, Irelia has a better teamfight while still maintaining a decent capacity to duel (certainly not as well as Tryndamere, but not as far off as you'd think).

This is the biggest issue I see with Irelia. She's incredibly too safe. There are match-ups where she is punishable. Champions like Jax can outright beat her, champions like Nasus can farm pretty decently against her and with wither + frozen heart, you destroy a bunch of her DPS. Malphite fits this same criteria. However, it does not matter because her Q spam farm acts as an escape hatch from bad situations for her, so she can resort to out-teamfighting Nasus and Jax, and just be an obnoxious split-pusher against Malphite without the intention to ever interact while keeping waves shoved and looking for picks. She has too much safety and if you removed her ability to auto clear waves like this (even reducing her Q's damage by half vs minions; or giving it a static cool-down after using it on so many minions) would do far more than any numbers nerf you could ever possibly apply on her.