This is the difference between the diegenetic and non-diegetic view of character abilities. You want the character's abilities to be determined by the preferred story structure, even if those abilities don't make sense on their own. I prefer the character's abilities to be something real to the character. Something he knows he can do. The wizard knows which spells he can cast, and presumably knows he can only cast each spell once. But for a fighter to know he can't swing his sword like that again for the rest of the day once he's done it, or he can't make that perfect shot again for no clear in-character reason, well, that'd be weird. So unlike the wizard, the fighter character loses knowledge of what he can do. He becomes a puppet of the limitations that the story demands of his abilities.
Mind you, I'm not at all against some form of meta-currency to give you that extra oomph just when you need it. Fate points, plot points, karma, bennies, etc, I do like having that something extra to save for that special moment, and those exist outside the knowledge of the characters (except in Earthdawn obviously, where characters explicitly manage their karma). But that is an extra meta-currency on top of what the character himself is capable of, and what he knows himself to be capable of. But in D&D4, these meta-concerns infringe on the character's own physical abilities. And these abilities even have a special magic-sounding name, making it really more like a spell than a mundane ability. It damages the distinction between what the character can do and what the player wants from the story.
And those special moments in the movies, they could just as well have been a simple critical hit. Doesn't it hurt the suspense of the encounter when you know: I can still use my once-a-day encounter busting ability? One of the cool things about RPGs is their unpredictability. You can have the randomness of the dice create the drama of the story. When I played Earthdawn, the exploding dice meant that sometimes, due to luck, a simple d10 could roll over 20 or even 30. That move, whatever it was, was instantly epic, even if the player didn't plan it.
I grant you that class balance in 3.5 is seriously broken, and I totally believe you that 5 didn't fix it either. And yes, 4 is a lot more balanced, but balance at the cost of flavour isn't very good balance in my opinion. In the end, the core of class balance is this: in every situation, every PC has to be able to contribute something useful, and everybody has to get the chance to truly excel every once in a while. Not everybody has to excel in combat, unless your game is only about combat. Having one PC dominate combat is fine, as long as the others aren't useless, and the others get plenty of other opportunity to shine. Balance is only really broken when, as in 3.5, some classes will eventually be able to do everything better than everybody else, making everybody else obsolete. But forcing everybody to have very similar once-a-day powers is totally unnecessary.