I have fought and played this combo, so I know both sides of the coin. There's a near unanimous agreement that this combo is severely overpowered in one respect, and I strongly agree that it needs to be toned down but there are a few inherent flaws.

I will be very honest and say that anyone who says this team is not overpowered is full of it. I've played against many teams that have tried to counter us, and in several of those games they would gather their entire team to rush us, but they would be completely destroyed by Alistar + Heimer, and a lot of times they couldn't kill even one of our turrets. I'm sorry, but no hero or 2 man team should ever be capable of defeating all 5 heroes at once at an even level. I am saying this as a person who uses the Alistar + Heimer combo.

Getting that out of the way, even though this team is very powerful, thanks to the balance of LoL, this is only a gimmick team that has 2 extreme flaws.

1) This is a gimmick that essentially requires 2 heroes to camp a lane to succeed. This means your team only has 3 people to defend the other lanes. When I've played against high ELO teams, they would ignore our turret farm and 5 rush other lanes. Our 3 teammates were outmatched by their 5 and they were able to break all our other turrets. We've actually lost a game because of this and made me realize that this combo, although very overpowered, is merely a gimmick, and CAN be countered. Given this, I still think it needs to be toned down or addressed because of the amount of effort/difficulty needed to counter this is ridiculous.

2) If you are sick and tired of getting owned by Alitsar+Heimer or Anything+Heimer, play Twitch. Twitches' super hits ALL targets in a line, and a good Twitch player can destroy all of heimer's turrets in 6 or 7 shots, 9 shots if Alistar is healing. The one team that we lost against, had a decent Twitch player, but not even he knew that he could easily break all our turrets until about ~30 minutes in.

Essentially, this team is extremely good for pug stomping, but it CAN be beaten with an organized team. The trick is to not even bother trying to fight us, there's nothing you can do. Even 5v2 it's just suicide. The best thing you CAN do is to rush our other lanes and kill our towers/inhibitors before we can finish pushing/camping your lane.

I've played against a lot of Yi's, thought he was ridiculous at first, but I no longer see Yi's as a threat in my team games anymore. Yi is great for pug stomping, but he is mediocre for arranged team games because of his lack of snares, stuns, or traps. Then again I also dominate Yi's as Blitzcrank.