Yes, Zed should be able to 1v1 someone and be capable of killing them very quickly. This is what assassins do.
But he does so much more.
He has one of the most reliable escapes for any assassin, he has massive waveclear, extremely good energy regeneration paired with low ability costs. If he wants to chase, he can stick on to people for quite a while and do ridiculous damage. If he needs to escape he can just pop W, flash, maybe do a little juke with his ult. He has poke to die for, a passive that does MAGIC DAMAGE!!! (Because that's what every AD assassin needs: Magic damage. Makes PERFECT sense)
QSS on the carry will hinder your carry due to the lack of damage items. If your ADC MUST buy a particular item to help counter one guy (maybe more, since it basically cleanses CC), then who's to say the other carry won't just kill them? You have 1 time to use it, and if you waste it trying to survive against others, then Zed can just ult on in whenever he feels like.
Also, have you honestly ever seen someone with Zhonya's at level 6? If they have, then they're stomping Zed and probably don't need it just to counter him. If you're behind and you desperately need it to survive, good luck trying to get the farm to buy it when he zones you out. By the time you get one, he's already got a BotRK. Zhonya's will not let you kill Zed, even if it does give 120 AP. It won't solve the fact he can poke and zone you for days, it won't solve the fact he can still do tons of damage, even without his ult, and it won't solve the fact that once he gets lifesteal, he can stay in lane indefinitely, while you go oom every couple of rounds of abilities because you didn't get any mana items.
He's just too easy. First time I played him in like a year, I went 10/7/15 (against a Yasuo, nonetheless). Sure, I screwed up many times (hence 7 deaths), but I could easily maintain a presence and I could still execute people just as effectively. A guys that just picks Zed can be a decent annoyance, while a skilled Zed main is absolute torture to play against. I never do good as champs I have never played before (save for Vel'Koz. I don't know why but I love him), but the moment I pick up one of those champions, suddenly I do really well.
In that one game I played as Zed, I understood that there's not a very clear way to beat him. You go in, he W's away or ults on you can gets the kill. You try to gank, W away or ult juke. Try to play safe, he farms up, pokes you down, then tower dives you. Try to poke back, you go oom (if you rely on mana) and you're either forced to back and let him take turret or let him tower dive you.
TL;DR: Too safe, too good. As if people haven't stated it enough, Riot needs to do something about this. He is the exact opposite of "Healthy Assassin"