I love Zoe. She is such a fun champion to play with unique mechanics and a rewarding playstyle. However, she is one of League's most-hated champions due to how frustrating she is to play against. Despite having an overall 49% winrate and a low pickrate, she has a pretty big nerf on the PBE. I think this nerf is unwarranted, not only because her winrates and pickrates are reasonable, but because MR shards are being buffed and Morellonomicon and Oblivion Orb are being nerfed as well.
What Riot should be addressing is how frustrating she is to play against before touching her damage. Here's why people hate Zoe:
1) If you use a summoner spell in lane, she will use it against you for free with added damage and a speed boost. Using your summoners is a net power gain for Zoe, not you.
2) She gets free summoner spells from minions, and can win lane through a RNG Ignite or Redemption
3) She can hit you with a stun through a wall without warning that secures a kill for either herself or a teammate
4) She can "miss" her skillshots and still deal a good chunk of damage due to the trap on Sleepy Trouble Bubble, the AoE of Paddle Star, her W bubbles, and her empowered autos.
Here's what I would do:
Sleepy Trouble Bubble (E)
* While the projectile is inside terrain, the exit point is marked with a sparkle effect, similar to Kayn's Shadow Step.
* The trap on the ground no longer triggers on the first enemy to enter the area. Instead, the zone imposes the Drowsy effect (a ramping slow over 1.4 seconds) on all enemies inside it. The first enemy who stands in the zone for the entire 1.4 seconds triggers the trap completely, taking the damage and being put to sleep.
_Comments: This change gives enemies a warning before a Sleepy Trouble Bubble comes through a wall. It also makes the trap area less hazardous for enemies. It can no longer "splat" on the ground and hit someone who just barely dodged the skillshot, but it still allows her to deny space and sleep enemies who are stuck in that area._
Spell Thief (W)
* Moved to R
* Begins the game at rank 1, max rank of 4
* Minion balloon drop table now depends on ability rank
* Rank 1 (levels 1-5): Heal, Barrier, Cleanse, Smite
* Rank 2 (levels 6-10): Heal, Barrier, Clarity, Challenging/Chilling Smite, Exhaust, Ghost
* Rank 3 (levels 11-15): Challenging/Chilling Smite, Exhaust, Ghost, Ignite
* Rank 4 (levels 16-18): Flash, Ignite, Teleport, Redemption, Protobelt, Gunblade
* All cannon minions and super minions carry balloons, but only cannon and siege minions carry balloons.
* Zoe's enemies can stand on a spell shard for 1 second to destroy it.
_Comments: A lot of changes here. Moving Spell Thief to R allows the rank of it to be gated by level, so the kinds of summoner spells she gets from minions changes in different phases of the game. Early on, she mostly gets defensive spells that help her survive the laning phase, not kill her enemy laner. In the late game, those defensive options go away in favor of more aggressive and versatile spells like Flash and Ignite._
_By tying the balloons to cannons and super minions only, it makes balloons come more predictably and gives the enemy more power to contest them, since Zoe can't just one-shot the minion with the balloon. Enemies can stand on shards to prevent Zoe from getting them, giving them more freedom to use their summoners without giving them to Zoe, but also lets Zoe use that time to line up a skillshots. She could use a strong summoner to bait the enemy into her damage._
Portal Jump (R)
* Moved to W, max 5 ranks
* Cooldown changed to 13/11/9/7/5
_Comments: Moving Portal Jump to her W allows Zoe to "feel" like Zoe pre-6. She gets her long-range artillery damage during the majority of the laning phase, giving her a lot more options and damage early on in the game._
Overall, these changes address the issues I described. Zoe wouldn't get lane-winning spells for free off of minions early on and her enemies would have more opportunities to deny her from getting those spells or stealing their own. Her E trap is a lot more forgiving for her enemies and doesn't just hit them if they're nearby when she misses, and it gives the enemy a slight warning when she uses it from behind a wall.
Getting her Portal Jump and guaranteed defensive summoners during the laning phase would help smooth out Zoe's early game and make her more difficult to set back, but since most of these changes make her abilities weaker, it might be necessary to buff other aspects of her kit. Increasing the single-target damage of her Q (but not the AoE damage), increasing the damage of her E (since it's less forgiving), or increasing base stats like movement speed or attack range might be in order. The point is that the most frustrating parts of her kit offer reasonable counterplay and allow the enemy to get more say in what happens to them.