As much as people wanna call Zoe broken...
I just can't, in good conscience, recommend playing her to anyone.
She just isn't that good, especially compared to most other mid laners.
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Her damage isn't reliable, and is super telegraphed (meaning you won't land many hits against competent players).
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She has long CDs on her combo, and doesn't do any damage outside of it.
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She isn't mobile, and is very squishy -- she can't even exist in a poke lane.
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She's very easy to shut down and kill.
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She has very little waveclear, and is easily pushed in.
Sure she can do some high damage (one time) if she lands an E>Q combo, but that doesn't happen very often now that people know what to expect. Outside of that, she really doesn't have much going for her. Her W is nice, sure, but it's also unreliable.
But, really, why bother playing Zoe when you can play Lux and do the same thing, but better, from long range? You could also play Syndra, Diana, Akali, Fizz and so many other champs and do her job (bursting people) better than she could ever dream of and have an easier time of it all the while.
I don't get why people complain about her when every other burst mage (and a lot of just mages in general) is just better than her in nearly every way.