Hey OP, please explain to me how having CC stops AP Yi in a 1v1 situation. Because unless you're one of the very few, mostly non-mid champs that has more than one hard CC ability or you're ganging up on him (which invalidates a 1v1 laning situation), you have to choose whether you're going to block his nuke or his full heal. You can't do both by yourself with one stun.
And since "blocking" his nuke will result in him just doing it when the stun wears off instead, your only real choice is to block Meditate, which will at least set off the cooldown and prevent him from using it again right away. Since Meditate heals for silly amounts of HP and raises his defenses considerably, he's still likely to heal at least as much as a health pot before it gets stopped unless your timing is impeccable, and either way, you're still getting hit in the face by that nuke first.
So now you've pretty much got to choose between either not farming to stay safe from his nuke or wading into the minions and praying Alpha Strike doesn't hit you. Even if it doesn't, it's going to blow up all your minions which means you'll now be tanking his, which during early- to mid-game laning can hurt quite a bit.
You can't just wait for him to blow the cooldown on it while farming (and lol, his farm is going to be insane no matter what you do) because it's got such a short one that you won't really be able to do much in between anyway.
If you have a teammate come into help you by ganking him or whatever - good luck, because he's just going to ult out of danger as soon as they show up and get back in your face as soon as they leave. Even if you've somehow got the jump on him in a way he couldn't react to, he can just bust your slows and leave. If it's hard CC? Maybe he's got cleanse, or Mercurial Scimitar, or tenacity, or he's just going to Meditate and heal whatever damage you dealt to him while he was stunned anyway.
Late game in teamfights, he's got his team to protect him while he tanks your whole team with Meditate, allowing him to full-heal and re-enter the fight almost immediately, and he's probably got a Zhonya's Hourglass for further trolling.
So basically, unless your whole team is centered around killing the AP Yi and his team is dumb enough to let you, he's going to be horrible to deal with, and whether or not that happens, he's still going to suck all of the fun out of the laning phase and be more or less unstoppable.
Tell me more about this mystical "counterplay" of yours. And don't give me this "just counterpick him" baloney because not everyone plays ranked or draft mode, and even if they do, as other posters have pointed out, AP Yi can easily be selected after the enemy mid has locked in.