Wording plays a part in this. Calling them 'powers' or 'martial exploits' implies that they are learned or possessed in some manner. Not that they are ways of controlling the narrative.Only if you insist that that cool move is something that the character distinctly knows in game and not simply a meta-game construct, identical to an Action Point.
Secondly; the fact you have to choose between them as you level up - effectively choosing what your character does or does not know how to do - contributes to the 'character distinctly knows' mentality.
Thirdly; The fact you can choose when to use a power makes a huge contribution. With wizards there is no question that he's casting fireball because he (the character) wants to cast fireball. Yet with martial characters, you're saying that the character has no choice in whether he can lunge right now, or whether he can attempt a hit and run. The wizard's chance of success is determined only by the dice. The fighter's chance of success is determined by the dice, AND by 'fate' (where fate is the player's choice).
By forcing all character types to use the same AEDU mechanic, the game forces players to think differently about the situation.
In 0-3E, the fighter is trying his hardest all the time, and the dice determine the outcome.
In 4E, the fighter has to wait for the right opportunity in order to try his hardest.
It's a question of where the limitation is coming from. With wizards, the character is limited by his own abilities. With fighters, the character is limited by something entirely outside of his own abilities. That discrepancy isn't sitting well with a lot of players. It makes sense for Vancian wizards to run out of spells. It doesn't make sense for fighters to run out of opportunities.
Whether a player likes it or not seems to boil down to, "Do you like, or dislike, being able to control the story as a player in this metagame manner?"
The more I read about martial powers and action points being the player's way of exerting choice onto the story, the less I like them. This thread is making more aware of why I don't like them.
If we are handing over control of combat outcomes to the dice, why are we then including mechanics that allow us to control the dice instead? Why not have the dice determine when an encounter or daily power kicks in, rather than the standard at-will attack? That would fit better with the idea that the dice are determining the outcomes of the combat. It would also resolve the issue of explaining why the opportunity only comes up occasionally - the dice only roll that way occasionally.
You'd be left with a interesting balance issue.
Fighters might be able to achieve their 'dailies' multiple times in a day because the dice rolled well, while wizards would be stuck with their daily limit, but would have control over when to use their powers.