Because her abilities are fucking slow as hell.
Her q has one second wind-up time, very easy to avoid by just moving lefr or right if the enemy keeps focus on you and not talking with his girl on fb while playing the game. Anyone with less than 100ping can dodge it.
Combined with this, she is stationary during the animation, making hitting skill shots on her easy. And over 50% of the heroes in this game have dashes or speed buffs.
Basically she doesn't have a q in lane against people that understand her.
Next, her w is a targeted dash which procs you passive or ultimate tentacles. Its a half decent skill by itself, similar to irelia q.
Next passive, since I've mentioned it just now. Spawns random tentacles over the nearby walls.... Which reads as: free farm for the enemy.
You basically have a passive that lets the enemy get gold faster than you.
Even worse than her q.
Next e. Draw target spirit out. To begin with the range is shit. And it can be blocked by minions. If only these were the only problems with it.
It has a long windup time just like other skill shots( think blitz and thresh). Except.. Aside from range difference if any of those 2 land their q. The target is most likely going low or dies. In late game it just dies.
But illaoi is different. Her e provides no cc. Attacking illaoi lowers duration of spirit.
ATTACKING the spirit does reduced damage to targets. Which means, if you DARE to attack that the enemy can attack you and you lose the trade.
The only good thing is that you can proc q heal on it, and that's a minor thing compared to the disadvantage it brings.
And even in later game states. If morgana, lux, blitz, thresh etc land their Q. There's a very high chance for kill. Illaoi grabs spirit, you back off for 20s and gg, its like nothing happened
So, its like she doesn't have an e.
R gives her multiple w dashes. And spawns invincible tentacles. Fucking hentai plot. But you can easily just get out of her circle for a few seconds and you are fine. Just like going out of fiddle or phanteon ult. You dont fight in there and illaoi lacks the cc to keep you in it.
So in lane she has only a W and R.
She was designed as a teamfight hero. Yet acroaa all servers. She has the lowest kda of all heros, 1.7 or so. Hence generally she gets like 1-2 kills/assist per team fight. Compare that with darius or garen. Their numbers are much better.
So, you got a shitty laning phase and a shitty team fight phase. No cc and no escapes.
So, if you want to win as illaoi you must always be better than your enemy. There's ni option for equal ground. You start with a disadvantage from minute 1