I main support, and as with any ranged support, harassing with autos is not uncommon. And you can quickly drop the minion aggro if you duck in and out of the brush. The extra damage on auto-attack is really not necessary for this (she already can be very oppressive as a support).
You have to ask yourself what you're trying to accomplish with the change you propose. And not only that, but what is the problem? Her current passive is fine. And you shouldn't really be relying on it for anything. It just means that after she dies, she still has one last shot to deal some damage. This is very situational and doesn't really apply to trading or harassing she does in lane. So her power during laning is actually completely independent on whether she has this passive or not.
With that in mind, your suggested change does nothing but give Zyra more early game power. You just gave her bonus damage on auto-attack, from the start of the game, and tried to compensate by making her late game weaker. That makes no sense. If you add early game damage to one place, you need to take away early damage from somewhere else.
Zyra is in a fine place as it is. She doesn't need more early-game damage than she has right now. I feel like you're trying to fix something that isn't broken, and making that fix in all the wrong ways. If he passive feels useless, that tells me you aren't relying on that passive damage for anything. But she also doesn't lack damage outside the passive. So rather than replacing situational damage with strong, guaranteed, steady damage, I'd go more along the lines of suggesting some manner of utility passive instead. Just to throw something random out there, maybe she could have reduced death timers, and they could call the passive Springtime Thaw or something like that.
