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Agree with everything you just said qutie strongly: I especially agree with how looking at how there is no inherent advantage to iniative helps you realize that the EV created by iniative is purely a product of the opponents misplay; primarily their ineptitude to play 'correctly' against your hand range.

EG; this includes stuff like calling with KQ on an ace high flop with the right pot odds and a wide enough raising range; or even raising it; given that the raisers range isn't actually that likely to have an ace, even though them taking the iniative may suggest they do).

An example of exploiting iniative I have used frequently is against a fairly tight player we play 3 handed with who 3 bets a fairly normal range but if you cap preflop he will give up overcards on the flop for fear of domination; hence the extra small bet invested causes your opponent to make a large post flop play error because said opponent has not thought about how he is being exploited; he is a victim of iniative, a man made concept that does not actually exist in a game theory model, but only in the minds of the blissfully ignorant.

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Couple of points:

1. Yes, 'initiative' exists only in the mind, but hell, the entire game of poker is a 'man-made' mental game. It's not a physical contest. So all mental concepts become real.

2. You claim 'initiative' does not exist in a game theory model. I believe it does. And it has to do with risk. In your example of capping pre-flop and folding out the three-better on the flop, what has happens on the flop is that your continuation bet puts the first claim on the pot. If he has nothing and he wants to 'reclaim' that pot, he now has to put in at least two bets. In essence he has to risk more than you did, and most people tend to be risk-averse. Now folding automatically with overcard(s) in this situation is incorrect, and is the sign of a weak player, but is understandable in this context and is a good example of the value of 'initiative', whether it's just purely a mind-game or not.

3. I also want to try to understand why 'initiative' exists. In other words, why don't we all just play as if we don't remember what happened the previous round, especially if the previous round was just pre-flop play which really doesn't narrow your hand range down much for the trickier players. (Understanding why it exists is not important to play good poker, as long you know it's real and how to exploit it.)
And my theory about why it exist is that we tend to fight much harder to keep what is ours than to take something away from someone else. A man may risk his life fighting off a robber, but would never think of stealing something that is not his. This is also true in the animal kingdom where a smaller animal will defend his burrow much more fiercely than he would invade another burrow, and hence can often drive off a bigger invader.
Hence when we show aggression early on (pre-flop), we are laying initial claim on the pot. Whoever has put in that last bet has laid the last claim and it is recognized as such by both parties. Now both parties will also recognize that this defender will be more tenacious in defending his claim. This oftentimes will have the effect of getting the other party to back off of and letting the guy with 'initiative' claim 'his' pot.
Now is all this merely a psychological by-product of a more basic mental mechanism? Absolutely! But it is nonetheless real and very important.