The main issue with Elise are her cooldowns

You're probably right, but her kit is so loaded with stuff I think higher cool downs are necessary, she'd probably get even more complaints about being too op if she were spamming all of them.

The thing is you can't burst someone with one rotation you either have to run away or die.

I think it's a waste for her W to be weaker because it's Aoe, since the buff monsters now no longer have small companions. I think it should spawn sort of like a pet, then allow you to control the target it attacks. But keep the interaction where you can have it pounce on enemies if you switch to spider and Q.

Even with max CDR her damage skills aren't that strong. They have no scaling and the ratios are pretty low. Unless she gets fed she will fall off a cliff.

Her damage skills need better scaling.