Should akali's E proc on-hit effects of new passive and Q instead of getting more damage?

For those who haven't read the new changes, akali's new passive is a 2-hit combo: the first basic attack heals her scaling with AD, and the second deals bonus magic damage scaling with AP, then the effect goes on CD.

I understand riot wants to deliberately slow down the attack patterns of assassins, but would akali's kit feel smoother if her E would proc her Q again, and also proc her passive for enemies hit (whichever one is currently active)?