Well, it is worth noting that Heracles, Thor, and Hanuman are all gods.
Two of them are Demigods, technically, but I don't think that changes much. All three are fairly typical "heroes" from ancient myth. Most heroes from myth and legend had varying degrees of divine lineage as justification for their power. So did the monsters they fought, which are now used as normal D&D monsters (the original Hydra was Heracles' cousin twice removed, or something like that). Thor in particular had adventures very similar to what a high-level D&D character might experience. There is also the fact that high-level D&D heroes can fight gods, or become demi-gods or gods themselves. The idea of a strict boundary between god and mortal is more the product of monotheistic thinking anyways, and doesn't have much bearing on polytheistic myths.
I'm not at all opposed to the idea of high level fighters doing superhuman things, but don't think you need to draw the lines so far out as Thor and Hanuman. At 20th level, not that my campaign ever goes there, your average (average?) fighter under my rules would probably be able to out run a horse, leap over a small building, climb a wall of ice, leap from a 200' precipice and survive the fall, and smash a stone (or a wall of force) with his bare hands. He can inspire a small army to fight with a fearless passion. His hands may well be lethal magic weapons. He can quite possibly win a bare knuckle brawl with a 3 ton giant, and drink an ogre under the table and that isn't even to begin to discuss the powers of the heirlooms and artifacts in his possession. He's no longer merely mundane; he's a superhero. That's the expectation.
None of that would give him narrative power necessarily. I'm inclined to see 'narrative power' as something of a red herring here.
I think the best way to think about this is in terms of non-combat problem-solving ability, and the ability to create new situations. Let's look at the Fifth Labor Heracles faced (which I referenced earlier): cleaning out the Augean stables in a day. This is the kind of task that can either be solved by weeks or months of mundane labor (rendered impossible by the time limit), or can be solved through clever thinking and special abilities.
In D&D, the Wizard could solve this problem in a number of different ways using various high-level spells. A few move earth spells and walls could redirect the river like Heracles did, or the Wizard could try summoning up a large volume of water directly.
On the other hand, a high-level Fighter isn't really given many options. Traditionally, D&D doesn't really give them any tools. Performing superhuman feats of strength, such as digging canals to redirect a river in a couple of hours, generally falls outside of the reach of skills in D&D. It could be done with a complex skill check, but D&D hasn't ever encouraged people to allow superhuman feats, and gives little advice for doing so. Furthermore, such things would exist entirely outside of the Fighter's inherent abilities.
So there is a lot of problem solving that a Wizard can do as a Wizard, but very little that a Fighter can do as a Fighter. Anything a fighter can do is classless and generally available, while Wizards can do things only they can do (and those things are generally better than the classless alternatives). Since various similar non-combat problems can crop up quite regularly in a D&D campaign, this can become an issue.
