On PBE, Xypherous gave a pretty good explanation as to why hybrid items can't coexist with hybrid champions (in a game with mostly non-hybrid champions) without either having to be underpowered. (here's the Rioter Rundown, since specific links to posts seem to not be working for me properly)
Here is the specific quote:
It doesn't seem like hybrid items add much to the game because it seems to flatten hybrid characters entirely and lock them to a small subset of items.
Let me walk through this a bit:
Let's say no hybrid items exist - but the character is a hybrid character and all their skills have AD and AP ratios.
This hybrid character can then build any item in the game and benefit because it doesn't "waste" any statistics from any AD or AP item. This character could build Zhonya's and Bloodthirster, knowing that their DPS would go up. They can't build crit - but they could effortlessly pick up a lot of mage utility items and sustained AD items.
However, add hybrid items into the game, like gunblade. Do you expect the item to be better on hybrid characters than non-hybrid? Well, then it has to give both AD and AP - in better ratios than most other items. Inevitably, what this does is bind the above character to only building that hybrid item.
If that character is OP with that hybrid item, the character gets nerfed to accommodate for that hybrid item and the character is balanced around that hybrid item existing -or- you nerf the hybrid item and then you get to the point of why did you even add that in the first place?
So what happens? Well, now - said character loses the ability to build non-hybrid items when hybrid items are strong. It basically takes a character that could work well with any item in the game and collapses them down to whatever hybrid items you've made. The strength of hybrid characters is that literally no item is bad on them and they can forge builds that are way more powerful than most people can imagine.
When you make decent hybrid items, you basically destroy these builds and lock them into your hybrid items as they are by default, the most efficient build path. It gets worse when down the line, if the character gets rebalanced assuming the purchase of hybrid items as now they are locked into the item's existence.
This is why I've continuously stated my preference for Kayle's old AD --> AP and AP --> AD conversion passive. She could build whatever she wanted and she always ended up as a hybrid character that needed to use all her spells and her attacks in order to succeed. I think our current 'hybrid' characters tend to build either AD or AP because nothing in their kits forces them or causes them to benefit from both AD and AP compared to the power of % penetration.
The more you focus your damage type into a single type of damage, the more powerful % penetration becomes and thus, it's mostly pointless to not focus on a certain type of damage.
That said, I don't work on champions at the moment so these kinds of thoughts are mostly theoretical at best.
It isn't just Akali that's an issue (although I did get a facetious "The answer to "why not" is always Akali" out of him. :P)
The issue is that when hybrid items are strong, ALL hybrid champions have to be balanced around needing to build hybrid itemization (instead of being supremely versatile--which is arguably half the point to playing a hybrid champion.) When hybrid CHAMPIONS are strong, hybrid items have to be weak...and then the hybrids just build AD or AP because Last Whisper or Void Staff scale their damage better than building AD+AP both could ever dream to.