The only thing that is unhealthy about Fizz right now is his ulti. And not the size of it, that's ok. But the way it attaches to people, even when they are seemingly out of range of the initial cast. That's beyond idiotic.
Now, how to play vs Fizz. Again, we have the typical bronze mentality "oh Fizz can dodge everything and one shot everything". Oh please, Leblanc, Vladimir, Zed can also dodge everything. One shot? Rengar? Kata? They can also one shot. The thing people need to realize is that the game doesn't start and end at the laning phase. Just because you screwed up and got all-in by Fizz and died isn't the end of the world. There is still the mid game and the late game, where Fizz isn't as strong as you think. The fact that a squishy champion has to enter into the entire enemy team to deal any meaningful damage means that he is super vulnerable to CC, damage and death. He falls off hard late game, and his only saving grace is maybe he can find a good flanking potential, where he won't waste his E to enter, and use it as an escape or as a damage tool. Same for champions like Riven, Katarina, Zed etc. All squishy melee champions who have to first wait for all the CC to be blown out before doing anything meaningful.
As far as the laning phase goes. Fizz isn't as annoying as you think. He struggles way too hard in the early levels, where you will either sacrifice cs or his life, if you play correctly. Also, since you know that Fizz has a strong all-in at level 6, why aren't you buying a Negatron Cloak / Hexdrinker? Seriously, this tilts me off the face of the earth. Everytime someone complains about a champion, I see their itemization, which doesn't change no matter the enemy, the state of the game and what not. "Oh, I'm playing Lux so I'll get Morello first no matter what". Goes back at level 5, buys Lost Chapter, gets all-ined by FIzz at level 6. 'OH MY GOD NERF FIZZ SO BROKEN NO COUNTERPLAY", when you could have just bought a Negatron Cloak and just nullify most of his damage. Having an Exhaust is also really helpful.
Seriously, people need to be smarter. A champion all-ins you at 6? Maybe build more defensively. Maybe buy a rune page where you have more MR + HP. Maybe sacrifice some CS and trust that in the late game, you will be better than him.