I don't think ezreal is broken or op. But man does he get under my skin. I've been banning him every chance i get just so i can get a break from him.
He's so safe and difficult to catch while putting out great damage. And when you finally do kill him it doesnt feel like an accomplishment, it feels like i just walked through hell.
I don't think he's at all mechanically healthy for the game. He benefits from harassing you from complete safety every second and a half. This same harass will continually drop AoE slows and be spammed at you until you either Flash in an attempt to kill him or die. There's really no escape once he gets going.
I mean, Ezreal is annoying, but... 
Hes like that buzzing fly that swat away from your screen every 5 seconds. but i dont find him annoying enough to ban. I ban champions that engage hard like xin or jax
I ban Kennen because he's an annoying shit to fight in laning.
