true that it isnt, I was just demonstrating the effect it would have on akali is similar to what you were saying. Also it doesnt always have to be common to be effective.
Looking at your item concept i think it looks pretty solid except seems like a pretty good bonus for the 2350 price tag. comparing this item to mine, on a purely damage based hybrid champ (akali) the AP and AD bonus's are relatively the same give or take depending on how you build. But your item will do more dame than mine, making it more for high damage champs.
I prefer to play a lot of bruisers, that is where this item concept came from. Thresh, the newest addition to league, was the champ that originally made me think up this item. I prefer to play him as a bruiser more than as a support as he does have the damage potential and tankyness. The idea behind this item for him would be that you can build tankier while still getting the full spectrum of damage output. with the current items we have available there really isnt an item that can help you be tankier AND do damage for both damage types. And adding one that is balanced (as it would essentially combine 3 roles) would be difficult. The bonuses from this would allow u to pick up say...a iceborn gauntlet for armor and dmg, this and haunting guise's upgrade (cant remember name) for health and damage, wits end/mercurial scimitar/abyssal scepter or something similar for MR and be able to have the damage needed for late game while having a bit of tank to suppliment it.
tldr: need more hybrid options for bruisers.