Why play adc?
They aren't viable. Crap damage, Crap Mobility, Countered by literally everyone. About as much range as all the assasins and fighters.
All you get out of them i a strong level 1 to 3.. Anivia is better for botlane.
They used to counter tanks, but even when you are 1000 gold ahead of a tank you can't kill them, and you can't kite anyone.
You can't flash away and reposition from anyone, because they have that + a gap close. You can't run because they all have cc and all run faster than you. You can't survive their burst even when you buy tank items. You can't carry because you rely on your team too much. They are just not viable at all.. there is no reason to pick them at all. Vayne being a mild acception