I'm a Teemo, AP Yi is a problem?

No it doesn't, all it says is that you don't know how to use teamwork to win a game. If they're split pushing, get your whole team together and push a lane to force a teamfight. It's AP Yi, he can't even really knock down towers.

Besides, in your own example at the start you said he stood between two towers not caring. Right there, you should have stunned him. If he walk up to a tower? Stun and kill him. By yourself or with your team, it doesn't matter. If you stun him, he can't heal or run away.

I swear, there's no voodoo secret to this or anything, hard CC shuts Yi down hard. That's why he's not a very good champ.

And for the 3rd time, LoL isn't a "everyone on both teams mindlessly run to mid to 5vs5 and die" game.

Your theory about why it's balanced requires no fights to ever occur except 5vs5's in mid.

There's a word called "split push" you obviously never heard of. The odds of having an army of people ready to spam CC to stop the heal isn't that high.

If you were hoping someone like Soraka would use silence to do it? Well, odds are high that he used ult to kill her in 3 seconds long before the heal was even needed.

How would he do that if he is AP, if he is AD, then his heal is the last thing he leveled, it barely gives armor, and you can honestly DPS through that. Why did you not push after winning your 5 vs 4 while he split pushed then?

There's also a word called "strategy," seems you've never heard of it either.

AP Yi is a one trick pony. Alpha Strike then....... then.... then.... okay now I can Alpha Strike again.

Let's put your split pushing AP Yi, who can't knock down towers very well in the first place, against a defending.... let's say Riven, shall we?

Riven: Valor.
Yi: ALPHA STRIKE!
Riven: Broken Wings.
Yi: Waiting for Alpha Strike. Might as well Meditate.
Riven: Ki Burst. Oh look... the Meditate is stopped.
Yi: Still waiting for Alpha Strike.... time to Highlander awaaaaaaaaaaaaaaaaaaaay!

Conclusion:

Failed back door attempt.

Next?

As an avid AP Yi player, I would have to disagree because his heal is so easily countered. If you don't have anyone on your team with a stun, silence, knock up, knock back (possibly taunt... haven't been taunted while channeling his heal) then your comp is bad. In addition, a morellos or ignite also shuts down Yi's heal. To be a good AP Yi requires very good timing because if you don't get a kill off that first alpha strike, then you have 7-9 seconds of almost no damage to the enemy team before you can do it again. His heal is what makes AP Yi viable (with the new items, he's now EXTREMELY viable).

1. Stun him when he heals, otherwise if you have no cc you deserve to die.
2. Watch as he gets murdered.

if he goes to split push, that means you can send someone to stop him.
if they have a cc, they win. any argument to the contrary means you don't have enough wards to keep track of him, and have failed in some other far more significant way.

or you can 5 man push onto 4, win easily (if you can't win easily, you are behind in some significant way, fix that) and i guarantee 5 can push faster than 1.

in team fights you can completely ignore him and be fine. his alpha strike has low damage for the high CD it's on and it only deals damage.
or tag him with 1 cc and win. you have 5 people, any number of which can have a hard cc. they have that many minus one. rejoice.

actually thats a really bad example

This tactic is countered by wards, timing, and map awareness.

If he wants to tank a tower while your team rushes another lane so be it.
If he wants to push a lane then all your team has to do is push it back.
So what if he runs or heals? There's gold everywhere, go get it or just hit him while he heals, ignite or cc him if you can. May as well. If its a bad idea just retreat and force him to choose between healing and fighting. Healing is the main defense of carries anyway. Lategame alot of carries will heal to full in 2 or 3 minion hits. Its nothing special.

If youre worried about backdooring your team is either too slow, can't initiate and win fights, or you all just arent paying attention and are getting roflstomped by someone who is