Illaoi should be able to attack and destroy her own tentacles.
Here's why: If I come back to lane and my jungler comes to gank -- my enemy will have cleared all my tentacles by now -- I will run past the minions sieging my tower to try and catch them. Now I'll have to take a round-about route because of minion block and my tentacles will spawn all willy-nilly. Regardless of whether or not the gank was successful, I will be stuck with horribly placed tentacles until the end of time, or the enemy laner kills me because of my bad setup. The only situation in which I could get rid of these tentacles is if my enemy laner is merciful enough to kill them, or I leave my lane for 60+ seconds which is not something Illaoi was designed to do. She is the set-up queen (if I recall correctly). She should at least be able to edit her setup to maximum efficiency.
Another example would be if I walk into mid lane from the river and a tentacle spawns in the brush there. I won't get a tentacle attached to that wall anywhere near the lane for as long as it exists.
Of course, Illaoi shouldn't just be able to freely edit her tentacles at will. What would be the point of positioning, then? So maybe tentacles would have to be alive for ~10 -- 2 seconds (decreasing with level) for her to be able to target them. And then maybe she could get a 50% refund on her current passive cooldown. It would also encourage her to build up tentacles in mid-lane (for the eventual team fight) and then go back and kill tentacles in the river to reduce her cooldown for the more important mid-lane. This would increase her skill cap beyond just "hit E, R, smash W until someone dies."
And lastly, it would give her a partial escape ability with her W when disengaging (which she is horrible at). Or to dodge skill shots. (A really neat trick would be setting up a tentacle in the ghost camp and then hopping over the wall to run away. She would only be able to do this twice, though, per tentacle. And she can already do this if the chicken are up, anyways).
It would be interesting if hitting an own tentacle with W could heal you up as if you had hit an enemy with a tentacle (since the tentacle won't be able to attack anyone, then). But that would be abused, I think, because of her W's low Mana Cost. Even if it only healed you in combat, and especially since its cooldown is 4 at all ranks now.
Tl;dr: I only want to be able to kill my own tentacles. So much more could be done with that concept, though.