He gets played as an AD mid by anyone who is smart. The reason being that farm is more accessible in mid lane, and is easier to get. In an even lane he can powerfarm without having to worry about getting jumped on by the enemy support, and doesn't really have to worry about anything but jungle ganks, since he can stand back and just farm.
He also has easy access to blue in mid lane which supports his spammy farm heavy play style - furthermore you can actually build a tear on mid ezreal without saying "okay so I'm an adc but I'm gonna do no damage til at least thirty minuets". Stacking tear is easier in mid because of the access to blue I mentioned above, and you don't have to worry as much about your early damage output because you can both stack faster and not feel like you ned to be /the adc/.
You also have really nice map pressure by just staying mid, pushing, and using your ult. - Until you stack tear you can stay mid and get assists with your ult. If you power stack tear like this and get blues you can easily have your muramana at 20 mins. Which is going to mean you're doing a LOT of damage with your Q - by then you should also have a complete tri-force if you are power-farming you'll only need 223 CS at 20 mins, and that's assuming you get no kills or assists at all.
Mostly it's just cause it's a safe lane for ez to be in and it makes it easier for him to power farm without worrying about being jumped on or scaling too slow.