n fact, she is actually still quite relevant even when behind unless she's 0/15
No, she's really not. She's one of the worst champions in the game when behind. She contributes nothing but damage and tankiness (only 1 slow in her kit for utility, no pickoff but the delayed slow on her E, no engage). If she doesn't stat up, she's contributing less than almost anyone else.
Flash is a summoner spell with a 5 minute cooldown, that's not counterplay.
It's funny you mention flash, given that she's dependent on it for a good ult. Most of the time, she's reliant on walking in towards you slowly to ult. The counterplay to that is obvious: walk backwards while hitting her, or have one person stun, root, or even slow her to completely fuck her ability to get into range to do anything. It's that simple.
Also, flash is counterplay, by definition, since it's something active you're doing to respond to an enemy. It's also effective counterplay versus Illaoi, given that she has no way to follow-up if you flash when compared to other champions. If you flash away from a Riven, she can dash and follow you. If Renekton dives at you and you flash, he can have a second dash to follow. If you flash from Illaoi, she's not getting onto you without a flash of her own. She just doesn't have the tools.
Instead you just listed general things to do against literally any AD bruiser.
There is a strong point to be made that the general things to do against AD bruisers are way, way more effective against Illaoi than they are against most AD bruisers. Most of them have some response to general counterplay; Illaoi doesn't. Illaoi gets counterplayed; she doesn't counterplay anyone else.