Akali needs some kind of a heal in her kit

I've been playing the new Akali for.... let's say a while now. The new nerf hit me like a pile of bricks. So after several frustrating games in pbe i kinda got that she needs the heal otherwise you're FORCED to buy several bruiser items after gunblade and zhonyas, cuase they're just not enough. So i went with and , but you can see where I'm going with this. Akali is an assassin and the combination of those two items isnt a pick for an assassin, so I thought to give her passive a heal. It would go like this: After harming an enemy with one of her abilities, a circle appears. once she exits it her next basic attack will do extra dmg and five her hp. it scales with lvls and hitting a champion with it has an increased heal so Akali should go and do these risky trades.

also her W. I think it stays too long on the battlefield. If you decrease its lifetime you could still give her the true stealth mechanic, cause the dive must be precise and calculated.