Corki atm, has only 1 problem and that's extreme mana costs. Apart from that he is a solid adc.
Corki is actually pretty strong in s3. Good mobility, plus poke, plus burst, plus an aoe armor shred, plus a truedamage steroid. He's better than ez in my opinion, who gets played a fuckton, but he has a much higher skill cap and more item dependency because of the way his truedamage steroid works.
Ezreal definitely isn't as strong as he was in S2 (thank fuck), but people are very used to playing with him so I guess it stuck with people as a fall-back adc or for people who very rarely play adc, their go-to champion. I think a similar thing will happen if caitlyn gets nerfed to the point where she is no longer considered to be hot shit. She will still see a lot of play because people have been spamming her for so long that they aren't comfortable on anyone else.
.
If you're running a lot of champions that shred armour then why do you need corki? Surely a team like that would prefer to have a champion with an AoE AD ult like twitch, MF or even graves to abuse the lack of effective armour on the enemy team.
I'm kicking some ass with cho'gath despite multiple people telling me he sucks