Zed and Azir aren't the problem. Low counterplay burst champions don't feel fun to play against.

While Zed and Azir are the most competitively successful because of safety, honestly any champion that kills you in 3-4 buttons in under 2 seconds feels terrible to play against. That frustration is amplified when it's someone with an escape like Zed, Azir, Leblanc, or Fizz and ganking them essentially is off the table, leaving the laner which more than likely has a bad matchup against them to fend for themselves.

Super high damage melee guys like Nasus and Darius don't feel that bad to play against. You see them coming, they have to commit, and there's counterplay. These burst champions on the other hand can zip in, kill you, and get out almost risk free with little time to react and not much counterplay to what they're doing.

It would be nice if 100-0 assassins were changed to work in another fashion. What if Zed's shadow teleporting crazy outplay potential was turned up to 11 and his burst toned down? He'd be way more fun to play. Honestly current Zed just sits around and wave clears and plays safe, then once he's farmed enough, starts deleting people. It's really boring, honestly. Assassins are only fun when they're getting fed and almost never fun for the people fighting them.

So IMO champions should have to choose. Burst or safety. They shouldn't have both. Just my opinion but I believe that's why all of these champions are so hated. The champions themselves would be a lot more fun if their other strengths were played up and the burst aspect was toned down. LB is this cool deception mage but in the end she just plays like a derp slamming her face into the other guy and dumping all her spells at the same time. That's not interesting. This is missed design space that's getting wasted on something so simplistic, in all actuality.