3-bet pre-flop or check-raise the flop?

[StellarWind]

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"Provided that you assume that Villain will autobet the flop there can be no "loss of value" that everyone keeps talking about."

Assume you have AA and your opponent has KK. If you 3-bet pre-flop, there's a good chance your opponent is capping (if 4 bets is the cap). Now assume that the flop comes A-K-5. There's a good chance that the flop gets capped as well. If you didn't three bet pre-flop, you would have missed out on two bets.

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First, unless Villain is a special type of dumdum (a few exist) he makes money off his preflop caps when averaged across your entire range of 3-bets. Cappers have better average hands than the people they 3-bet.

Second, there is a certain number of raises after which the cowboys will "get it" and just call you down. This number of raises is player-specific, but I don't see why on average you wouldn't get an extra raise postflop to make up for the raise you lose preflop. If the cap on the flop stops the show, then we can just start up again on the turn until he finally slows down.

Third, in this specific case I would greatly prefer to have called preflop. It's going to be much harder to figure out that KK is no good after I just call preflop. Even if he knows I never 3-bet my possible hand range is still larger and the chance of AA correspondingly less.