"Ahri has a rather hard time assassinating if she even misses one part of her kit."
Oh, please. Her Charm literally forces her enemy to walk towards her while being unable to take action, her W and Ultimate automatically lock onto their target, and her Q goes through targets, so nothing can body-block it.
"Syndra also has to hit literally everything."
Syndra's E is the only ability in her kit that needs to be aimed and can be blocked. Everything else will hit anything in the area she designates or is unit-targeted, meaning all she has to do is click on what she wants to use the ability on.
"Meanwhile zoe picks up free summoners"
That is false. The Spell Shards Zoe collects are not "free", they must be earned. Zoe needs to collect them. She needs to last-hit a minion that spawns less than one-per-wave and then go over to it to collect it. Alternatively, if an enemy Champion is irresponsible enough to use Summoner Spells or item-active while Zoe is around, Zoe has the opportunity to try to safely collect it. Considering it's right there for everyone to see, you have every opportunity to stop her from collecting it. Use you area-attacks, point-and-click abilities, crowd-control, skill-shots; it's easy to stop her if she's going for it. If Zoe has a Spell Shard, it means no one stopped from collecting it. She earned it.
"zoe can be more spammy"
Zoe more "spammy" than Ahri. Oh, jeez. Well, I've already pointed out how Ahri's Q has a superior cooldown for most Ranks. How about their E's next? Their crowd-control skill-shots that are crucial to their combos. Zoe's E: 20 / 18.5 / 17 / 15.5 / 14. Ahri's E: 12. Ahri's E has a shorter cooldown at every stage of the game.
"However most zoes arent hitting at minimum range. Max range with 100 ap is 425 plus 150 is 575."
Why are you taking calculations using her maximum range? Your complaint, and I quote, was about Zoe "killing something in under a second with just q". Zoe cannot achieve maximum range "with just q". To achieve that range, she needs to incorporate other abilities into a combo.
"if zoe only knows how to fight at minimum range"
That's exactly what I'm saying. Zoe does less damage at closer range. Ziggs (and most other Champions) do not have this limitation. If Zoe wants to achieve her full potential, she needs to land long-range skill-shots (which most people would agree are more difficult than short-range ones) and she needs to use other abilities to achieve that range (which provides opportunity for skill-expression). It's not "just q".
By the way, claiming that "ahris pool of mana is lower than zoes" when the difference is literally only 7 mana is rather manipulative, especially consider Ahri's gets greater mana regeneration than Zoe as a game progresses.