In my games, the Martial power source isn't just a way of saying "not magical", but is in fact another kind of magic, an actual POWER SOURCE as such.
It's just not an external one, like Arcane and Divine. It comes from within the user, from his or her own body, life force, and driving inner passion.
Given the eight power sources listed in the PHB, I use the following as my barometer for where each of the power sources comes from:
- Arcane power comes from the mystical energies of the Feywild.
- Divine power comes from the sacred energies of the Gods in the Astral Sea.
- Shadow power comes from the dark energies of the Shadowfell.
- Elemental power comes from the raw primordial energies of the Elemental Chaos.
- Primal power comes from the inherent magical forces of the living earth itself, of the actual physical world.
- Ki power comes from within the person, arising from the practitioner's Spirit or Soul.
- Psionic power comes from within the person, arising from the practitioner's Mind or Psyche.
- And finally, Martial power comes from within the person, arising from the practitioner's Body or Heart.
So it works out really well. Eight types of power, from eight sources. There are five major planes in the cosmology (Astral Sea, Elemental Chaos, Feywild, Shadowfell, and the Physical World), with five power sources linked thematically to them. And there are three archetypal divisions of a person's Self in a lot of classical thought and psychospiritual models (most typically stated as Mind/Body/Spirit or something similar), with three additional power sources linked thematically to each of those. Every base is covered, and every power source has a logical point of origin and flavored justification for its existence.
I kinda think it was intended to be seen that way, because it lines up so darn well.
So it's not that martial equals mundane, it's that it is another source of real magical POWER, just coming from within the core of physical strength, vitality, and passion in the wielder, rather than being drawn and molded from an outside source.
The wizards and clerics and illusionists and elementalists may all delve into studies of the other planes and call upon forces beyond the physical realm to form their magic and alter the material universe...
...and the druid may tap into the natural power of the earth for her magic to gain the ability to change reality...
...while the monk connects with his inner spirit to harness his ki magic to empower himself with supernatural capabilities...
...and the psion masters the depths of her mind to such a degree that she can magically transcend mundane limits...
...but the warlord or the fighter draw directly from the deep well of their own life force and physical potency, the pure strength of their bodies and their presence, to produce a personal form of magic that affects the world around them in ways which go far beyond "normal" or "non-magical" means.
In my opinion, the warlord isn't just shouting and "boy, is it impressive, so I guess I'd better be healed now". His words have actual, "magical" power, coming from that inner, bodily power source which is called martial, to distinguish it from the mind-based psionics or the spirit-based ki.
I see the martial characters as being, essentially, very very similar to monks and psionicists, just with a different flavor, and a different ultimate focus on which internal resource they are tapping into.
All eight power sources are MAGIC. Five external sources, from the five planes of existence, and three internal sources, from the three archetypal aspects of a whole person. But none are mundane, none are analogous to just the sort of normal, scientifically-explainable stuff that regular folks in our day-to-day modern experience can do.
Seeing the martial power source as being merely the same thing that soldiers in real life do is really doing a disservice to the concept, I think. Mundane onlookers in the D&D world shouldn't watch a martial hero in action and think, "Hey, that guy's really good at fighting. I wonder if our local pugilist champion could take him?" They should think, "Holy crap, how the hell did he do THAT? That's impossible! That had to be some kind of magic!"
The warlord isn't just some Joe Blow army NCO who knows how to yell at his men and get them motivated. He's a MARTIAL HERO, an iconic, mythic WARLORD destined to be named in bards' songs for years to come. He isn't just "inspiring" you to get up through the content of his spoken words, he's altering reality through the raw power of his own inner might, greatness, and glory, and his own confidence in that power.
You being awake to hear it is irrelevant.