Zed has counterplay. CC him until his W or R duration are over, and he's fucked. A Nautilus support, a Leona support, a good Morgana mid/support, etc. Pressure him in lane to keep him behind and he'll get his Duskblade powerspike too late, by which point your team, if they've played their cards correctly, will have some decent objectives and items under their belt.
Zed has mobility, sure. His W can be used as an engage/poke and an escape if it's back up in time. His R serves the same purpose. The only difference is the amount of damage he can deal. If you have a trashy support and no tanks, expect to be shredded. Just by his WEQ. No defense=more offense on the side of Zed. That's on you. If you get your tank to... tank... his Qs, then your team won't take as much damage, meaning that he'll have to fall back onto his R to get a kill, by which point, if you CC him a la Nautilus hook or knockup, your team can melt him.
Zed has damage, because he's an AD Assassin, first and foremost, and an AD Caster. His abilities scale off AD, just like Talon's, or Kayn's, or Rengar's, or Kha'Zix's. He has far more in the way of itemization, and he has far more in the way of utilizing his kit properly in teamfights to get some poke off if he can.
And don't exaggerate his shadow range. If he uses W first, he's going to switch to that shadow first, and it has a fairly decent range. If he ultis first, he's going to W after to dodge any CC and then swap back to his ult shadow so that he can EQE the rest. That has an unlimited range, yes, but he has a one-second delay before he can return. Your teamcomp should be prepared to CC him.
And what CC does he have? The insignificant slow on his E? Invalid point. Shaco, Leblanc, and Rengar (empowered E) all have better CC than him. Hell, if you have a Rengar on your team, just have him waiting in the wings. The moment Zed goes in, get your Rengar to hop on his Ionian ass and p00f him. I've never seen a difference in damage between jumping in as Kha'Zix or just hiding in a bush. Rengar, fair point, because Riot fucked him up badly. Shaco and Leblanc? I'm absolute shit at Leblanc, and I've never played Shaco, so I can't speak on those two.
But Riot himself has said that Zed has what every assassin should have. Both thematically, kit-wise, etc. He has decent mobility and damage. Rengar doesn't have that level of mobility save for arguably his ultimate, which even then is a kamikaze. He presses R, jumps in, and hopes that he does enough damage, right after dying. Riot designed Zed to be a healthy assassin. Decent outplay potential and equally decent counterplay potential. Like one, you must learn the other. Zed mains defend Zed because they know his strengths and weaknesses. We know that once he's CC'd, he's fucked unless he buys a QSS, and even then, it'll be on cooldown for the next teamfight. He does horribly against good ranged mages like Azir (if played correctly) early game, and the Azir should use that against the Zed. Push him in, stop him from getting his Duckblade powerspike, get your own team ahead, ggez that's one less person to worry about.
, he has a great mobility and sure, he has no a good cc, but you know what?, shaco has not either, a box that need to be 2 seconds until works is not a good cc, not for teamfight at least.