Overall she is a bad champion.
Her Tentacles can be easily killed, her Q and E are both dodgeable, her W has short range and can only be used as a gap closer, and her Ult can be walked out of. Anyone with any sort of skill can reliably dodge her very slow Q and E, this cuts her damage by around 80-85%. Her W is a strong ability when used in conjunction with her Passive or Ult, but if the enemy is proactively killing her Tentacles its almost useless. Her ult can be strong in a teamfight but is completely useless if they walk out of it or if they just CC, alternatively they can just focus her and out damage her sustain.
She is designed to build damage in order to deal damage but with no inherent tankiness she is required to build a lot of tank or die before she can use her abilities. She is incredibly weak to kiting, she has no MS boost and her only gap closer has barely more range than her AA's.
During laning phase she is either bullied out of lane and made useless or she bullies her opponent and runs out of mana. She is super easy to gank as she has no CC or Mobility, if you stay away from her Tentacles she is a free kill. Due to mana problems she is forced to trading only when her Tentacles are up and she has her W, if she tries to poke someone down with her Q she will be out of mana before they are even close to being dead. That is a big if because most likely they will step slightly to the side and dodge her Q.
Her E is a fun mechanic but ultimately useless, they either run out of range and kill the Tentacles without taking any damage or they will hit her two or three times to make it so she can't proc it. Even if she does proc it, the mana she needed to use in order to deal enough damage is almost never worth the damage she will get off it. Any decent player can dodge the Q's fairly easily as they are very telegraphed, once you understand the timings you can even continue to farm while you wait for the next Tentacle.
As if all that wasn't bad enough, her Tentacles actually give away her presence whenever she is near them. Makes it impossible for her to sneak up on anyone and at all times her opponents will know roughly where she is. They are also useless unless used with her W, so without any way to use her W her Passive might as well not even exist, the only thing they do is give free Gold to the enemy.
Illaoi can be strong against certain opponents or against players who don't know how she works, other than that she is one of the weakest champions in the game. I'm not talking damage-wise, she can deal a crap ton of damage very quickly, but overall her Weaknesses outnumber and outweigh her Strengths. There is almost no team comp where you should choose her over another champion, her role can be easily filled by several other champions who are both viable and reliable.
If they changed her Passive to be more reliable she would be a lot more viable, but that would create a lot of balance issues. Ultimately Illaoi is just a weak champion, she is fun to play and definitely can be good in the right hands, but overall she is just too weak.