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AK is leading more than 50% of the time preflop. Therefore we raise. Raise when you are winning.

Strategy 2 sounds like a good way to go bust against 2pair or a set.

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Sure, that can happen. But you can lose or go bust in any hand in which you don't have the absolute nuts. I understand that it's wise to raise when you're likely ahead, but to always do this seems overly simplistic. My goal in poker isn't too win the maximum number of pots possible, but rather to win as much money as possible overall. Therefore, I feel a case could be made for limping in with A-K, because when you hit the hand on the flop (which will be far more often than some small pocket pair nailing the set), you're going to be able to extract a lot more chips from your opponents, on average, than if you raised something like 3 times the BB before the flop. I feel like this is especially true on internet poker, on where people like to limp in with A-anything.