Simply build tanky, and get massive healing from your tentacles.
I... what? Of course you're going to get a larger heal if you're building full tank. You have more health to heal off of. But you're not going to do the damage you should be doing if you build full tank.
You have early lane harass, by making the opponent have to avoid every single one of your abilities which will not only heavily damage them but heal you.

You can win a 1 v 5 even at the lowest health.
That is very, very unlikely. Situational at best.
People will try avoiding fighting Illaoi in tight spaces to keep her from ulting and tentacles popping on walls (not like there aren't walls everywhere), but wait; they appear anyways.
So do people with Poppy. And she has a fuck-ton more utility and more reliable damage than Illaoi.
Her tentacles are her main source of damage. And you can always walk out of her ult range.
In the end she's a heavy damage unkillable tank that really needs some "changes".
Hey everyone, let's take a champ with a 46% winrate who's already weak as shit and nerf her(basically what you're saying)! Because that's a great idea.
Also, Darius does everything you described she does and does it better.