Jungel Olaf And Black Cleaver

I've been playing Jungle Olaf alot the past few days and I really like rushing on him, but I haven't seen any other people use\recommend it except I think ZionSpartan in the top lane. I actually see reccamened more but Black Cleaver is much better. I think Black Cleaver makes sense as a core item because:

1. Flat health is always good on Olaf do to his Ragnarok passive and sustain especially with .
2. the 40 attack damage is just the right amount to make his damage relevant throughout the game (with Ragnarok in late game); so he can focus on tank.
3. The %20 CDR works fantastic with his kit by speeding up clear, increasing sustain with W, and increasing how often he can use his true damage E.
4. The rage passive activates on physical damage rather than basic attacks like Frozen Mallet; meaning that when he hits his Q he get a slow AND a speed buff; which makes ganks all the more deadly. Not to mention with Stalkers Blade and his Q he has 2 slows and since slows don't stack anymore it doesn't make sense to add a third.
5. The Cleave passive works great with his attack speed based kit and make ganking tanks more realistic. It also helps late game since the whole team benefits from the armor shred.

I've been rushing it as my second item after Cinderhulk, but I'm going to try rushing at least , if not the whole thing, after Stalkers Blade but before Cinderhulk. Since Cinderhulk only has 300 health, and the +25% bonus health doesn't really do much before you have another item or two, the hp from Phage is comparable for a similar cost. In addition, you get the +20 AD and the Rage passive which helps with early ganks more so than Cinderhulk. With Olaf's Q and the +20 AD his clear should be fine with out the immolation passive anyway so it makes sense on paper for ganking, farming, and dragon\scuttle control.

Anyways I was wondering what other players think about a Black Cleaver rush so I decided to make a post here. Sorry if this is in the wrong sub forum, it's my first time making a post about gameplay.