Starting from the Q width, to providing 30% armor pen to multiple people at once, to late game half HP burst if landed E on anyone + passive applied and essentially made 5v4 with one skillshot). The only real weakness she has no escape tools, meaning that she should be easy gank target. But wait, if you come and gank you'll get double killed, because she deals EVEN MORE dmg when outnumbered. If you somehow, by some godly miracle manage to kill her without dying, guess what, she'll still be able to outduel your top laner and deal more DPS. It's like playing vs Vayne with AOE dmg, the scaling is ridiculous and there is close to nothing you can do about it.
The only way I can see Illaoi bringing to the balanced state is for her to get Tentacle Smash width reduced, less dmg on E and maybe be affected by Frozen Heart (so that there is at least one item that you can itemize against her). I would also think to code Tentacle Smash to be considered an auto attack, so that you can maybe get Thornmail and let it retaliate damage a bit.
P.S. I understand the the whole concept of ''pick AP lane bully'', but Malzahar was the only one who could counter her and be a competitive pick and he's just gotten the nerf. https://www.champion.gg/champion/Illaoi (scroll down to ''champions that counter Illaoi'').