Now compare this to mages late game who drop one or two spells and the wave is gone.
sadly none of the mages you listed can clear ALL the minions with 1 spell. 2 yes. Sept Eggnivia because of her ult. But you are missing the point. Mages are supposed to be known for their wave clear and AoE damage (typically). And assassins for there single target blowing up power. Zed can do both. He can wave clear just as fast or faster than all of the mages you just listed. AND he has insane BLOWING UP abilities, AND he is one of the most mobile champions. AND he never goes OOE. He has the best of both worlds. with no down side at all. He has WAAAAY to much going for him, very poor counter play, and insane snowballing.
Its not a matter of how many spells it takes to clear the wave. The point is he can clear it faster than most the mages you listed, and almost all other mages.
For example.
Vieg: If he is wave clearing he has 1 and only 1 AoE ability to do it with. This ability CAN not hit all the minions. in VERY rare cases does this actually happen. There for he has to wait for it to come off CD witch it has a long cd. think 8+ seconds at max rank. Slower than Zed
Vlad: same case as vieg, has only 1 decent wave clearing ability (unless he wants to waste his W which has a VERY long CD and could kill him if he gets sneaked attacked) SLower than Zed
Vel: has good wave clear, clearing pretty fast if he has 2 stacks of his W (i think its his W) Just as fast as Zed
Ziggs: again good wave clear but the main source of it is his Q, which he has to cast atleast 2 times to clear the entire wave, some times more if he cant 1 shot the melees. Just as Fast as Zed (some times slower)
Eggnivia: Very good wave clear (the only one on the list that can do it in 1 spell) Just as Fast as zed
Xerath: Very good wave clear. but again has to at least use 2 spells. Both have 6+ second CDs Just as fast as zed
Zed: W-Q-E clears the entire wave late game. Just as fast if not faster than some of the mages. An assassin should not be able to do this. Not to mention that all his spells have very low CDs at max rank.