I thought of this too, but are you then unable to use the Hex by itself when it is off cooldown and your ability is not? It could definitely work if you choose between attaching an active to an ability instead of a hotkey, but that opens up for more possible active items you can use at a time, and I think the limited slots is a part of the balance (in that you can only have 4 active items at a time).
Definitely worth it to look into.