And why do you think YI is not ridiculously OP?
AP Yi gets his burst off and becomes useless between cooldowns. Gets fed in lane, carries games, yes, however 1)6 items Yi is much weaker than most other champions with 6 items and 2)A good player won't feed in lane - as soon as he sees that he's losing, he will play a lot more defensively.
AD Yi deals more damage than AP Yi in late game, however his heal is way weaker than AP Yi and a good team will simply burst him down before he does any real damage.
And both AD and AP Yi have a few shared weaknesses:
1) The heal can be interrupted very easily - in ranked, players will usually be smart enough to get stuns/knockups specifically for Yi. And most of these stuns/knockups will have shorter cooldowns than Yi's heal.
2) Fiora syndrome - firstly, Yi has no CC in a game where CC is very important and second, Yi needs to get close to deal damage, but doesn't have the tankiness to survive in the range where he is the most effective. Building tanky? Tanks in LoL are supposed to be the ones that can remain useful even without building damage - Nautilus, Maokai and so on have lots of CC, Shen and Rammus can force enemies to target them instead of the carries , Renekton hurts even without building AD. A "melee carry" such as Yi will benefit much less from tanky items since he is built around the idea of dealing lots of damage with lots of items.
I could probably say more, but I think I said enough and I'm not really that experienced. I was around level 21 in EUNE, then moved to NA and almost reached silver (I know I could, so I count myself as silver) and moved to EUW where I am still lv15-ish. It's odd now seeing all those Yi players. In ranked, even as low as Bronze I, most players considered Yi a weak champion.
Put simply, Yi is newbstomper. He depends more on the opponents lack of skill than the players skill. Which is why he's only effective in low level games. If someone on my team feeds Yi, there's not much I can do. But when I lane against a Yi, even if he ens up with more cs, I consider myself the winner of the lane because I know that if I didn't feed him kills, I will end up more useful than him.
Also, it seems to me that low level players can't organize a decent 5vs5 fight. Which is where Yi's weakness becomes the most obvious.
Goddamnit, now I need to play LoL, I took such a long break from it.
edit: Oh god, I remembered why I had to take a break, low level games are so bad.