Curious about Sterak's

Been getting more and more back into League, and looking at some of those items I've neglected looking at since League has changed so much. This one is a bit curious for me. I notice it in some guides on Mobafire, and even some guides that include both it and Tri-Force. What's extra curious is none of the guides really say if you get one, you need to get the other. Or even that you should, or that they synergize at all.

Anyways, back in the day I found doing my own research usually yielded better results than any guides. So I did a little digging on numbers which is why I started poking around guides.

So I noticed people mentioning tanks are a bit loaded due to high base attack, and people abusing that with certain builds. This made me curious "Which tanks?" "Also, what scales with base attack?"

That led me to this (I still haven't gone through masteries)

Base AD Iceborn Gauntlet Lich Bane Sheen Sterak's Gage Trinity Force

I already knew Tri-Force, I didn't notice Sterak's did, or that it'd synergize with Tri-Force for an extra wombo combo til looking through it.

Anyways so again, this led me to guides that don't really mention it either, and of course as mentioned checking champions base AD+Scaling (for reference) http://leagueoflegends.wikia.com/wiki/List_of_champions/Attack_damage

Anyways, I found the one nearest to the top of the heap that I play (Jax) not the best but someone I already have experience with, and as a bonus already build Tri-Force on.

Anyways, hard to say that it went well, I won but the whole game was a bit messy and it wasn't anything spectacular. Still, the overall base stats of the item (that much attack WITH that kind of defense) feels extremely efficient. I almost never see this item though.

I imagine it being ridiculous on Illoai/Udyr. Why don't I see it more? Even in some guides it's missing, the synergy with Tri-Force is almost always left out, and honestly, on these champions it seems like an absolute requirement.

Is it that good on those champions. More specifically, is it that good on Jax? One thing I also noticed in the case of Jax is that he has VERY high damage scaling based on BONUS attack damage (100% on leap strike, 50% on counter strike) but this adds to BASE attack damage rather than bonus, meaning by building these you're losing out on spell damage. In that way it almost feels like they negate their own bonuses.

For the same reason it wouldn't be as strong as initially thought on Illoai (though still definitely worth). So as far as I can tell, the best target for this item combination would be Udyr. Interestingly enough, the last Udyr I played against (who did well also) didn't build Sterak's but did build Tri-Force.

Thoughts?