Before getting into the suggestion itself: while the proposal isn't bad, simply throwing out an idea for a solution, without stating what kind of problem you're trying to solve in the first place and how it would be addressed, isn't the most helpful way of giving feedback. I get that the Boards, and probably many more players, are likely aware that Zoe is unhealthy and perhaps still a little too strong, but even so, that nonetheless doesn't really give all the context needed to understand what exactly your solution aims to resolve. While I personally like your idea, ideas in any creative medium are a dime a dozen, and have no intrinsic value of their own until proven: what is more important here is the process of reasoning that got you to the idea, and more specifically here the statement of the problem you're coming up with ideas to fix in the first place.
Now that that's been said, I do think it could help to remove some extraneous effects from Zoe's kit, including the impact damage on her E, as she currently has a lot going on and gets to deal a lot of burst even when she's not landing her Q, which is supposed to be her prime source of damage. It could also be interesting to make the ability more of a damage bonus for teammates, rather than herself, though that could also push her towards bot lane and require balancing there too (which wouldn't necessarily be a bad thing if Zoe could remain viable mid). Overall, limiting her non-Q damage sounds like a good idea, as she already has several cheap and relatively safe means of dealing damage, and is frustrating as a result of it.
However, I'm personally not sure if this would really fix Zoe's largest problems: in my opinion, the fundamental issue with her playstyle is that she's designed to one-shot, but also can personally lay down hard CC that completely prevents her opponent from reacting to her one-shot ability. Effectively, all else held equal, landing a single spell on a squishy can guarantee her a kill, whereas her range and utility give her plenty more options to escape punishment. Her kit takes the core combo of burst mages to an extreme, along with the associated frustration of getting killed during hard CC, while also adding in the low cooldowns and high ranges (and therefore the safety) of artillery mages. Because of this, I don't think her Q and E can ever truly be healthy together: even if her E stun were changed to stasis, it would still leave a fraction of time where her target would be a sitting duck, and that is enough to take a lot of much-needed counterplay out of her kit. Because of this, I think Zoe could perhaps be healthy as either a one-shot champion or a champion with long-ranged hard CC, but not both at the same time.