Let's look at Zoe from BOTH angles. Hopefully we can find some core issues like that.
"Zoe are high SKilcAP chmPA"
"ZOE faSTESt ASAsIN"
"DDINEy ChAMp"
Let's take a break from the one sided, and inane, arguments surrounding Zoe that tend to resonate in this echo chamber called the League of Legends Boards. To get a few things straight, let's go over some gameplay general concepts with Zoe.
Zoe's Q increases in damage with the distance it travels, dealing 80% damage to things caught in the blast radius and 100% to the target it detonates ON.
Zoe's early game is largely considered weaker than her mid-late game, because of the amount of long range burst she has.
Zoe's amount of cc and zoning in her bubble trouble make it good for skirmishes.
Zoe's usage of her W means that she, indeed, has a very high skill cap to play at her FULLEST potential.
Let's address the issues most people playing against Zoe have.
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Zoe's burst pattern feels unfair, because I can't see into the Fog of War. Her sleepy bubble trouble landing guarantees that I get one shot from a screen away.
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Zoe's damage in general is sky-high. Too much for the long range mage she is.
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Zoe's insane amount of power through her W makes it extremely unfun to play against her.
To address both 1 and 2, if compared to other artillery mages and assassins, Zoe actually does both jobs at once. She can provide long range damage, and she can also provide a quick assassination on the enemy ADC. Here's where things actually become a little less one sided. While Zoe can do both tasks effectively, she can't do either of them to a high level. It is this balance of Assassin and Mage that sets her apart, and makes her perceived as "Overloaded Infuriating".
Let's look at their damage. Xerath can deal massive damage at long range, at the expense of mobillity, just like Zoe. However, his range far surpasses hers, through both his basic abilities and his ultimate. In this sense, Zoe can't really compete through raw damage at range.
When things get closer, Zoe has her passive. However, Assassins dominating the meta, like Talon, don't really care how much damage you can deal in 2 seconds, because they can deal more.
The synergy of Zoe ensures that she has to use both aspects (heh) at once in order to become an effective champion. That means she fills the niche of a "Ranged Assassin", but still doesn't do a perfect job at it. For one, she has to actually land her E. Second, she has to actually land her Q. Finally, if she doesn't weave her AAs into the damage, she misses out on what usually is the deciding factor between a kill and 300 health.
Arguing that such a short pattern of massive damage isn't healthy is true. However, Zed does the same thing with his W E Q Electrocute. The point is, Zoe isn't unique in the "Unfair Burst Pattern" argument.
Finally, arguing that her W provides too much utility is both true, and not true. Zoe can't pick and choose what she gets. That means that both the person playing Zoe, and the person playing AGAINST Zoe, both have to think about where they're going to use their summoners. "Playing against a specific champion shouldn't mean I should adjust my playing style." Do you cower against walls to cover your vital points when not against Fiora? Do you buy Sweeping Lens as a Top Laner just to fend off Teemo's wards? Plenty of other champions introduce increased difficulty in playing your own champion through their own mechanics, and that's nothing new.
Let's address the counterarguments that many Zoe mains have.
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Zoe has a massive skill cap, so she's justified in having so much power. It just means they're good.
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Zoe's early game is weak, so that more than compensates for everything else. Just take advantage of that.
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Zoe's W means that she needs actual thinking to pull off her high-octane playstyle.
Let's discuss them.
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Zoe indeed has a massive skill cap. It's very hard to land a Smaller-Than-Ezreal's-Q sized skillshot, especially when you aim it back and forward. To those of you complaining that you get all the time: Get. Good. Dodging skillshots is not hard to do. However, getting hit with an E means that it becomes harder to actually deal with Zoe's Q, because you can't dodge it when you're sleeping. The argument of "Just get Mercurial" is valid, but is a poor argument. Building an entire item just to counter one champion that is usually in a different lane isn't very healthy. However, most of the skill cap actually comes from how early game is played, and how Zoe can react to Ws that appear, not from the difficulty in landing her E.
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Zoe's early game is relatively weak compared to other stages of her game. However, here is where the skill cap effect comes into play. A very good Zoe who procs 2 empowered autos and doesn't miss her Q will delete a third of your health bar at level 1. Of course, weaving in between minions is a good way to counter this, but Zoe's early game isn't the weakest. Of course, her late game isn't the strongest either, but it simply feels like it. In truth, good positioning will counter very long range Es. However, against most Zoes, you won't be facing problems in the early game unless you're getting hit by the stray back and forth Q for 100 damage or so repeatedly. It is still difficult to capitalize on this though, because most champions that go Mid Lane are usually weaker until Mid-Game.
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Zoe's W is indeed hard to use to its fullest potential, but it's not hard to just pick up a few hextech protobelts and rocket around dealing bursty damage. This is partially why it's so hard to shut down Zoe when she's supposedly weakest. A random redemption, a hextech protobelt, or even a heal can screw over the hard work you may have put in to make a favorable fight.
In general, both sides are lacking in their arguments, and both cherrypick arguments. Zoe may have a high skill cap, but it's mitigated by the ability to use her at an effective level even without the necessary skill cap of utilizing all 3 ignites or 3 flashes, or some weird hextech protobelt combo. Her ability to deal damage feels frustrating because it's a new way of dealing damage, but it is also Zoe's only consistent way of dealing damage. Good vision will do the same thing it will do against other assassins, and increase the amount of time one can react to Zoe's bubbles.
As of patch 8.14, does Zoe need a nerf?
My verdict: No, because there are other assassins that need to be addressed before Zoe at this point. Zoe fails hard at close up fighting, and that's what most meta assassins do now, and she can't snowball easily if you can dodge her Qs.
Good communication will ruin a Zoe's roams but that never happens so i guess Zoe is the queen of Midlane after all
EDIT: Since I didn't address this, I have in mind some changes to Zoe.
Zoe's skill floor isn't actually all that high, and her very top skill cap is pretty artificial, as it comes from knowing how to use unique item combinations and how to use them quickly and efficiently while in the middle of a fight.
As stated earlier, her early game is considered her weakest portion of the game. However, it's not actually that weak, due to her ability to use Q and proc its passive twice in a row. My only suggestion is to nerf the early game damage that comes off of either her passive or her Q damage to limit the amount of damage she can dish out, and leave herself vulnerable.
Another part of the issue is that she becomes ungankable in random intervals. If a bubble pops up, ganking her is gonna be hard, with an additional item/summ spell + movement speed + bubble damages randomly appearing, it makes it frustrating to gank her reliably. However, this was sort of addressed already with her E nerfs, meaning she can't repeatedly use E and Q in lane. Utilizing her mana costs can come in handy. Again, a good Zoe player usually won't do this, so there should probably be someone looking into that.