Please stop calling Zoe an assassin

If Zoe is an assassin, then Veigar is an assassin. Veigar has infinitely scaling stats, an ult that can ACTUALLY one-shot, a W that deals 100% AP and has a very short cooldown (that keeps decreasing over time), and an E that makes sure you can land your W. Veigar can deal twice as much damage and isn't affected much by creepblock or champion grouping because he has AoE, multitarget, and targeted abilities.

If Zoe is an assassin, then Ahri is an assassin. Again, mobile with her ult, and passive movespeed (which is suspiciously easy to proc). Her charm is ridiculously powerful level 1 (they should revert that charm duration increase IMO) and her E+Q can half-health you once she gets a Lost Chapter. Combo with the R + W damage (passive, you don't need to land a skillshot) and you're dead.

If Zoe is an assassin, then Annie is an assassin (I don't think I even need to explain this one).

Zoe has unreliable CC (that bugs out sometimes and just goes right through the target) that has very low range unless you shoot it through walls. Her Q does a lot of damage, yes, and it can deal a LOT of damage, but it's slow, relatively easy to dodge, and it's pretty difficult for Zoe to travel 2,250 units in about 1 second she has to recast her Q (unless she picks up flash from somewhere). With her E "double damage" proc you could, COULD get about 1900-2000 damage with max build. However that's without any MR and assuming you get a max range Q (leaving yourself completely open for the enemy team to jump on you). Also, her entire kit is destroyed by creepblock and if you're in a group of champions they can just block the Q for you. If you get hit by the E with no creeps or champions around you probably deserve to take however much damage she does.

Her ult is powerful, probably the most powerful part of her kit, but it does no damage and she can't actually dash anywhere because she will just jump back to the point where she cast it. She's psuedomobile. She has blinks and mobility but it's not much.

Zoe is meant to punish players for getting caught out. If you don't get caught out, there isn't much she can do and you'll find in fights that her Q's will be stopped by the minions in your lane half the time and you'll take no damage.

I thought Zoe was busted too until I played a few games with her, then I realized I'm just bad at dodging.