I main Zoe and even I agree her design is terribly flawed but not because she's OP. Zoe has been hit with a lot of nerfs and they have toned her down from when she was on launch. But her design (Like all CertailyToxic champs) is still really bad.
Zoe's Q doing a shit ton of damage does make sense because out of 4 abilities on her it only 2 of them actually have damage she has control over, her Q and her E. Zoe's W requires a spell shard to be picked up and without one its just a useless skill that cant be used so alot of that time that skill may not even be usable because of bad RNG. Her R does not do any damage at all.
So surprisingly the kit to me is fine and I don;t have a problem with it. what I do have a problem with is how up an down her flow in the game is.
Zoe is one of those champions where she gets ahead and does really good or falls behind and is useless all game, much like Yasuo in that sense. If Zoe falls behind her farming and waves clear are just so terrible that even if she has an entire lane dedicate to herself for just farming to catch up, she simply won't. Her laning phase I find is also very weak because how bad she is at farming, essentially i find any opponent who plays the range game or plays cautiously will get ahead if her. Bringing a tank mid lane vs her, like Cho or Gragas or even Swain also make laning for her a total nightmare because they can't be poked down with auto's as easily.
But when Zoe gets ahead, she gets so far ahead that she's pretty much one-shotting entire teams. She might have a poor laning phase but if she does come out of it ahead then its a total nightmare for the other members of your team, she doesn't need to one shot your teammates it's the overall damage she does when she's ahead that makes her scary. If she starts to roman and lands even one Q on your top or bot lane. Thats it, half of their HP is gone and that lane now has to make an emergency adjustment from playing aggressively to playing defensively. Her massive power spike allows her to change the flow of another lane so easily its frustrating not just for you but for everyone on your team, that power spike only gets larger and large the more assist and kills she gets from doing this (Can you imagine her ganking for pyke? full kill gold just for landing a Q). In team fights, all she has to do is catch a squishy with her bubble and land a Q and if that person doesn't die right away then they have to back. She knocks doer enemies like bowling ins one at a time.
What's frustrating to me, and most likely others is that with Zoe, again much like Yasuo, there is no in-between, she's either a stomp or be stomped champion and its frustrating for everyone. Its not her kit i find the problem, it's her flow in the game which is really out of balance and whack, this is typical for CertainlyToxic. I want Zoe to be one of those champions which can just be used for casual fun but she's not, she's a stomp or be stomped champion and it sucks.
That's just bad champ design.