Riot if you want to buff Taliyah, then giving her lower cooldown is the wrong way IMO
Coming from a otp, IMO her E cooldown is fine. What she needs is survivability.
She is a battle mage, but she starts with 20 armor and ends with 71 armor at 18. Meanwhile a Syndra, who is a burst mage has 24.7 armor at level 1 and ends with 82.5 armor at 18.
This is just a little comparison, but why would a battle mage have much less armor and survivability than a burst mage?
Either label her as burst mage too, then it's fine to change her general strength, or give her some survivability, if you want to keep her as battle mage.