Why does everything need to be labelled? There is no particular need to name the source of power for each thing, since we don't do much of anything with that information.
When I watch a fantasy movie, lots of times guys with swords do things that would be simply ridiculous and impossible in our real world. But nobody in the film gasps and says, "Oh, my gosh, that guy is using magic!!!1!!one!".
Martial characters in D&D need to keep up with wizards and cleric who throw fireballs and summon demons from the netherworlds. Those martial characters will therefore need to be capable of feats that would be ridiculous to see in our world.
I DO NOT CARE if that is called "mundane" or "supernatural." I care about the resulting functionality and balance, not the label. To make everyone happy, build the function, and for some subclasses call it "mundane" and for others, flavor it as some supernatural source.