I think that D&D needs to get away from the idea that martial characters are somehow "mundane", at least in the real world sense.
Joe Fighter might start out as Dirt McDirt, dirty peasant dirt farmer from dirt town, defending his dirt crops from kobolds with a rusty garden spade...but if he survives to see high levels then he is on par with the likes of Hercules, Cuchullain, or John Carter (on Mars) and punching gods out. This power curve is an inevitable function of having character levels and vertical advancement, and pretty much guaranties that high-level characters are superheroes.
See, everything in the D&D universe is magical. Everything. In this imaginary world, which is imaginary, and thus not bound to the physical laws of our own world, magic is a primal, omnipresent force of nature like neutrons and electrons are to us. Who's to say that one couldn't hone their body to the point where they can sprint at the speed of a coked up cheetah and lift houses? How can we truly know what the limits of human (mortal) potential is in a world that operates under different physical laws?
Also, we have to learn to accept that some things in D&D are an abstraction, and not meant to model reality in a way that stands up to scrutiny. People like this. There's a reason that more people play D&D than games with hit locations and armor as damage reduction. Take Hit Points for example: How many full-on axe blows does it take to kill a high-level fighter in D&D? I haven't done the math, but it takes more than it would any of us. This is because hit points don't represent physical damage. This is not a 4E invention either...this is straight from Gygax himself.
So if we accept that Hit Points are actually an abstract amalgam of mental and physical endurance, then things like martial healing suddenly make more sense. The Warlord yells at his injured companion, who finds the will to get up and keep fighting. Anyone who's ever had a personal trainer should be able to wrap their brains around that concept.
Yeah...some of you want to keep martial types relegated more to Conan levels than Hercules. But D&D needs Hercules if it is going to keep the game interesting for sword guy at all levels. Don't like that? Then cap character advancement at level 10 or so in your own games, rather than conforming the game as a whole solely to the sword and sorcery genre. Afterall, some of us want to be playing balls-out wuxia fantasy superheroes at level 20 and beyond.
D&D Fighters need to be magical. Hell, they already ARE magical. Their magic is merely internalized, whereas arcane magic-users shape the forces around them, espers manipulate sympathetic connections with objects and other beings, and divine casters act as material conduits for otherworldly powers.