What's wrong with them being physical abilities is that that's a dissociated mechanic. We know how physical abilities work, and they don't work like that
Firstly, martial abilities needn't be wholly physical. They can have mental dimension as well: courage, boldness, trickery, intimidation, and focus are among the mental abilities that a martial character might need to develop, use - and sometimes hold in 'reserve.'
Secondly, how do 'we' know how physical abilities of a hero work in the context of a fantasy world? Anyone here ever cut a giant's achillies tendon, killed a band of kobolds in six seconds flat, cut their way out of a purple worm? No. We can't rely on our workaday nerdly experience of 'physical abilities.'
However, even if we /were/ to do something that preposterous, it still doesn't support your assertion that 'deep reserves' must be 100% generic, and that exhausting your capacity to do one preternatural heroic stunt necessarily exhausts all such options. If you do a set of high-weight curls with one arm, the muscles of that arm are going to anaerobic and become unable to continue beyond many reps. That won't stop you from running.
So, even if your invocation of RL physical abilities were valid (and it isn't), it would provide counter-examples to your assertion, not support for it.
That line of reasoning having failed you, why can't you accept the official explanation of 'exhausting deep reserves' given in the PH1? And, even if you can't accept it, why do you do feel the need to substitute a dissociative one, given that you find dissociative mechanics unappealing?
You don't actually have to answer these questions, there. You might want to just stop and think about them. Chances are you have a reason that you, yourself, have not examined, and you may want to take a break and do that.
That's an apples-to-oranges comparison. Concentrating too hard on trying to read a textbook isn't going to physically exhaust your muscles the same way a game of basketball will. The idea of deep physical reserves
You're adding 'physical.'
The game is saying that you can't use an encounter or daily power again immediately (with the same level of effectiveness), despite having "deep reserves" that are available for other abilities. If in the real world I'd be able to spend those "deep reserves" on using the same stunt a second time, why is a fantasy game - with ostensibly greater freedom of action - placing a limitation on me from doing that?
The gamist reason is to enforce the kind of variety of action you see in the fantasy genre (and the broader heroic or 'action' genres). You don't see characters in genre acting like Gauntlet sprites and just whapping away repetitively. You /do/ see some 'signature' things that the character does, say, in most fight scenes, but they're not generally what they do at the big dramatic moment. Limited-use is a way of modeling that aspect of the genre.
In-game, the explanation of 'deep reserves' that may be compartmentalized is not any more difficult, intuitively, then they idea of fantasy-genre heroics, in the first place, nor any more or less valid or consistent than generic reserves.
These dissociated mechanics are the limits.
We've been through this. If you assert that limits make something dissociative, then Vancian is dissociative, and you're unwilling to accept that. Thus your definition of dissociative can't rest on limits.
The burden of proof that a non-supernatural ability isn't "generic" (though I'm not sure what you mean by that term) is on it to explain, not on us to presume. If something presents itself as being an ability found in the real world, and then changes the basic assumptions of how it functions, it needs to explain the what and how of what's changed.
I see your problem (well, one of 'em). Martial powers are presented as abilities found in heroic fantasy settings, not in the real world.
And, what I mean by generic is what /you/ mean by it. You assert - with no supporting evidence from the game itself nor from the genre the game emulates, nor even from reality - that the associative explanation for limited-use martial exploits given in the PH1 /can only be interpreted/ as generic resources that can be used interchangeably to enable any power, whether a Ranger's 'Crucial Advice,' that lets an ally re-roll a skill check with a bonus, or his 'Weave Through the Fray,' that lets him shift away when an enemy closes with him, for a particularly clear instance.
The issue isn't that "deep reserves" can't be spent to compose a sonnet or something - it's that they're presenting themselves as a reservoir of sudden physical prowess, akin to a burst of adrenaline, that pushes you to great heights for a particular task, but then leaves you too tired to do that again...except for performing any other task.
Again, you are adding restrictive language to the concept not found in the PH1, itself. You are changing explanation to make it dissociative. Why is it so important to you that it be dissociative?
Magic is explained, always. However it works within the context of the game world is implicit in what the characters know and can perceive. Even if you don't say precisely why each spell must be prepared as a discrete package of magical power, the characters still know that that's the only way it can be. Magic always has an in-game representation, and this representation is always associated because magic gets to set what its own limits are.
It seems like you're suffering (or quite enjoying) a profound double-standard here. Martial characters and Magical one are both characters from an heroic fantasy world. They are equally-weighted choices in the game. If there's a compelling genre reason to make them wildly disparate in effectiveness and importance, then, from the gamist perspective, those choices either have to very differently-weighted, or one character type or the other needs to be removed as a playable option. Otherwise the game becomes imbalanced.
You're splitting definitions here. If you want to say that fighter powers are a supernatural/preternatural/non-natural power, then just say that.
Look up 'preternatural.' It is not equivalent to supernatural or non-natural. And, yes, martial powers are supposed to be superhuman, but not supernatural. It may seem like a fine line, and it's probably a blurry one, too - so if it helps you avoid the dissociation you claim to abhor, imagine that there is a possibly-supernatural explanation at any point where you perceive a possible dissociation.
That simple solution, alone, should have kept you from ever complaining about dissociation, in the first place.