Why not use Active Energy gain, instead of Passive?
Note: I have not been playing or caring about League for about a half a year, so bear with me here.
So I came up with this idea for a character and the abilities function with the same premise as Akali. What I did differently; instead of adding a Passive Energy bar, I added an Active Energy bar. (Active Energy meaning collecting energy by fighting or with abilities that allows energy gain, but never out of combat.) However, I am no game designer so I cannot guarantee that this idea works. What may sound good on paper is not always good.
But as I see it, it would add a new set rule for characters like Zed, Akali, or whomever you want to name call. Simply put; you want to use your abilities, fight for them.
I believe if Riot prioritized Active Energy over Passive Energy, we can see new classes of ideas for energy champions. Maybe some needed balance changes.
Anyway, I will leave the idea to fly here. Take it or leave it.