if you play blind pick, deal with it. You cannot counterpick in blind pick, so don't complain if you cannot beat ap yi.
Beating ap yi is very simple. All you need is one disrupt skill or grievous wound-applying ability. Fizz is a hard counter to ap yi, as well as cho'gath. His meditate is on a 30 second cooldown until he gets CDR. fizz's grievous wound is a much shorter cooldown, and cho's knockup and silence are both shorter cooldowns.
Now that's not to say that ap yi wont still do a lot of damage and be an all around ******* in lane (because that's his job), but if you pick a counter (fizz, cho) he is not nearly the amount of trouble he would be than if you were someone like Ryze (who has no disruption for yi's ult).
TL;DR, play draft pick, counterpick, and suddenly ap yi is no longer as powerful as you thought he was.