So where is the best lane to put her? Well bot lane of course, as a support.
I feel like you've done this before CertainlyT 
Baka Red2 votesPlease explain two of your points; what true damage? And how is "capitalization on enemy summoner spells" repeating the past in any form? I thought Zoe is the first champion who in any way uses enemy summoners to her advantage.
Unreliable wave clear I understand; I found it hard even against Intermediate bots. Also, the length of CC is long, if nobody wakes the sleeping bear.
kargish3 votesThe summoner spells part is Zoe's strength alone, but the intended meaning behind is that bot lane is rich on summoner spells and she can often initiate a fight there with her sleep. The true damage is her E, if you get knocked out of the CC through damage you take a shitton of true damage.
Unreformed Shaco3 votesThe true damage is her E, if you get knocked out of the CC through damage you take a shitton of true damage.
No, you just take double damage.
She would make a good jungler if only her W worked on camps.
Baka Red2 votesLots of damage yes, but that is not "true damage" but "magic damage". Your incorrect use of terminology is confusing. Please try to be accurate about these matters.
Btw, that E doubles the damage like Unreformed Shaco said, but even that doubling has a limit of up to 220 + 40% AP at the time of writing this.
nm10102 votesI see you aren't familiar with the champion, the bonus damage on e is indeed true damage up to a cap of 220 + 40% ap.
Baka Red1 votesAh, well, I tend to trust Wiki page over 'just regular near anonymous board/forum writers' and that Wiki does not mention true damage. Well, I tend to believe Wiki over Forumites at least until I see contradiction between wiki and actual gameplay with my own eyes. I guess I will do that test today evening. Thank you for the polite reply. :)
Muzét2 votesUnreliable wave clear
Her wave clear is fine. Not close to LB/Ryze level. But definitely fine.
Insane burst (fuck true damage).
This. I won't EVER get it. I mean you know that the true damage is capped by her E and most of the burst you take from her Q is magical?
Zoe with 300 AP at level 13. Let's say she will hit you after a sleep from 1650 range (75% more damage according to wiki)
Both Q and E Maxed. Q damage: 160 (at level 5) [66% AP] + 75% = 280 [115,5%AP]
E damage: 220 [40%AP] = 340
So you would deal if an enemy had 0 MR: 1469 damage (rounded up from 1468,5) From the spells themselves. The true damage isn't as high as people want to think it is.
Long and hard cc
But delayed. You have the time to zhonya, reposition etc... And You get a jail free card once you get hit by any champion damage.
kargish2 votesThis is not to justify her kit and how to fight it, this is about how it functions better as a support than as a mid laner. Her wave clear is not fine for a mage, and her extreme early game damage allows her to be a far better support mage than anything else. It's the same with 
support, they bring extreme burst damage and CC compared to that of a standard support.
As with one of CertainlyT's previous creations this champion will most likely be a main support role rather than the intended mid laner.
Muzét2 votesHer wave clear is not fine for a mage, and her extreme early game damage allows her to be a far better support mage than anything else.
Her wave clear is fine for a burst mage. Who's got her kit's power on basic abilities. Clear exemple of that as a Battle Mage 
.
Zoe can easily kills ranged and needs a bit extra for melee minions. She have some power as support like other mage (I mean any mage can somehow "support"). But that's it.
For the one you quoted, the fact is that they all gain from going bot because they faced multiple enemies: Brand's R and Passive, Zyra's AoE, Morg's R. Lux is a special case because she can pick off a target and can give shield.
kargish2 votesThat is not true even the slightest. Nobody picks Brand supp because "they'll benefit from having 2 guys instead of 1 at level 6" they take it because it's oppresive and has supreme cc+damage. The same with all the other supps listed. Those guys can effectively zone the enemy adc alone, and it's the same with Zoe. You'd be a fool if you picked something supp over their main role, just because there is more AoE potential.
Not to mention if Zoe lands her 2k range sleep it's a guaranteed kill. There exists no counterplay in lane once you're asleep, regardless of what combination Zoe is with it'll one shot you with the true damage+Q.
Miror B2 votesNot just repeating the past, but "kinda" repeating the current theme. You have something that (from what I can understand) deals a ton of damage and little actual counterplay aside from "kill her before she does her job". In a way, she's just a summation of the preseason and all the downfalls associated with it.