waiting until the turn paradox, simple HEFAP question

[kamelion44]

My friend and I were trying to figure out how this situation helps you:

AA on the button, large field. Early position bets, everyone calls. HEFAP says to wait until the turn to raise, so that you don't price them in, and make their calls correct. In other words, wait until the turn to raise, so that they make a bigger mistake. If you raise on the flop, they're not making a mistake to call for their gutshots, two-pair draws, etc.

My friend was arguing against this, saying that if they're all going to call anyhow, how do you gain by waiting until the turn? I couldn't figure out a way to counter his intuitions...any help?