it's not all that odd really but her weaknesses tend to be burst damage and range, so a lot of common picks can delay a fight with her ultil she doesn't have the hp left to initiate properly without burning flash
her damage is very high, but only if you fight where she wants you to. Most people have learned to actually always be moving and to run away from her if she is nearby so that her ultimate is wasted
if you stay in a fight with her, her ultimate can and will likely kill you if you don't manage to dodge to safety
if we look at it as a worst case scenario (a 1 v 1 with only 1 tentacle), her damage would come to at level 18
500(ultimate) + 500(ultimate tentacle attack) + 750(E tentacle attack) + 1200(W) + 750(Q) and then another W for 800 to 1200 and another Q for 500 (the soul should be gone by then)
this is an extended fight of about 8 to 10 seconds and most of the damage is avoidable (tentacle damage)...i'm not even sure if that one tentacle would still exist from her ultimate after a few seconds, but you can see that the basic idea is to not fight illaoi when it is to her advantage
this is also using OPTIMAL damage where she hits both her opponent and the spirit(and my math isn't really even right because she doesn't melee the spirit)
in all though, using OPTIMAL numbers, that comes to 5000 to 5400 in damage over an extended 1 v 1 fight using just her base AD
although, in a team fight, she is likely to hook 2 to 5 tentacles...put simply, if she manages to hit your entire team (which shouldn't be grouping in the first place), that damage essentially multiplies by the effective number the longer she can keep you in her zone
so, if you stay in a fight, in her zone and let every tentacle hit you, that is how much damage she could do in about 10 seconds
if she is fighting someone like jax, however, his total will probably equal or beat her own due to his stun and inherent steroids
illaoi is useful in team fights, but it is best to try and bait her ultimate, so that you can move the fight and then finish her off
illaoi's best quote is, "I'm not into sermons...broken bones teach better lessons"
another issue with things is latency(as it is an issue with everything), but essentially, you have to know what she is going to do, fake it out while fighting and proceed to pound her face in
I actually like illaoi a lot as a champion, but she suffers from the issue champions such as yasuo, zed, fizz, etc have...except...not as toxic XD where there's a specific thing you have to do to fight them or it's impossible...yet hers is much more clearly....there to exploit
personally, i'm wanting to create a bruiser illaoi build so she isnt' unkillable and has much more decent damage, but as things are, tank is most efficient, AD is most fun
main I have learned a very important lesson with hitboxes.