What If Olaf's Vicious Strikes Was His Passive?

It could be activated when his hp drops to a certain level, and then placed on a cooldown so that there are vulnerability windows that his opponents can capitalize on. This way, his opponents can strategize to bait his passive or the Olaf player may bait his opponent into activating his passive during a fight. This also prevents him from healing off of minions when on top lane. It could be placed on a low cooldown so he can still sustain in the jungle. All of this would free up his e for another skill. I still don't know what skill that could be, but having a skill with a more immediate effect would make olaf a more fun character to play as.

Let me know what you think.