Anivia keeps you chilled under her ult, and yes QSS removes the stun, but hey, the damage...still happens.
Charm can be QSS'd, and it's up a few seconds later, not to mention she does not need to land charm to maximize her kit's damage. So long as she lands the Q, you will still take full damage that she can offer.
Cocoon helps, but Rappel can get her right on you if it should fail. Again, her full damage is still very much possible.
Cass can reapply her poison quite literally about 2 seconds later and continue. Yes, that time is vital and she could very well die in that time, however, it's on a much smaller scale. 2 seconds, or about 70 seconds. Also, should you you be in her W poison field, that stays and you're still poisoned.
Malzahar yes.
Brand is a burst mage, I don't see where you're going with this. You do not need to be stunned to get hit by most of his spells. Two are click spells, two are skill shots. You can remove blaze, but his passive isn't where his damage mostly comes from. At most you may QSS his stun if he used conflagerate to blaze you in hopes to get the extra pillar damage and even then it may still hit. If you QSS his stun after he used pillar to hit you, you've done absolutely nothing. Everything else is a click. You'll just remove the passive. Which he reapplies with conflagerate.
Morgana does lose these things, however she still has extreme utility to offer when these are QSS'd in the form of her black shield. She's also long range with her binding with a very short cooldown so she can just try again soon. The ult will have to wait a while, but the 3 second snare wont.
Veigar's event horizon is only for dark matter. The rest he can easily land and still one shot carries with. And, event comes right back up shortly. QSS...does not.
Annie still deals full nuke damage with her combo. No absurdly long CC, but still full damage. And, she can get that stun back in about one rotation, which isn't long given her CDs. QSS...does not.
Sona will still deal max damage with her kit even with QSS.
Even Malzahar is still a ranged mage. He does require to get into melee to be effective. And, fun fact. QSSing his grasp only breaks the CC. Not the damage.
I did not say QSS only works against Zed. It's that it impacts his kit far more than anyone else's. Everyone up there, save Malzahar and maybe Cass, has their CC and effectiveness built into their normal kit, not just their ult. Sure, QSS Annie's stun Q. Sure, QSS Brand's Q. Sure, QSS Morgana's dark binding. It comes right back up.
Sure, QSS Zed's ult/kill potential. It comes right back u-. Wait. No. You removed his ult entirely, like it never happened. Cass will still poison you again in a second. Malz's ult is still dealing it's damage. And yes, Zed can kill without an ult. However when team fights happen, the rest of these champions have a variety of options at their disposal. Zed typically has to ult or jump on a low target to really do anything. Not to mention Malz, who honestly is the most impacted second to Zed, has the option to do his combo on those with zhonya's should someone have QSS. Zed, does not and that's what late game comes to. Zed figuring out who he can and can't ult.
Also, with QSS and Malz/Zed, Malz's is CC. So even for the briefest second, the target is CC'd before they can QSS giving rhe rest of the team or just Malz himself time to do damage. Zed does not impact the target at all upon ult.
These QSS issues aren't about the 1v1's. It's about the team fights. It's simply fact that Zed is most heavily impacted by QSS.