I have an easy answer to all this stuff: ITS MAGIC. Dragons and giants exist because magic. The whole world is suffused with magic. Really talented people learn to use it to do extraordinary things. They call it psionics or ki or rage or divine power or bloodlines or spellcasting or artifice, but it's all magic.
I don't think anyone is arguing that the Mythic Martial is not magical in this reductionist definition of magic. It's just not that useful a definition.
IMO the Mythic Martial should access the "magic" that allows dragons to fly and stone giants to walk. It's power source is "world magic" based on exageration of the physical. It's definitely not traditional Arcane, Divine, Primal D&D spellcasting.
I really don't care what we call it but there is something different about what the Hulk can do as a martial -- super jumps, ripping up buildings, earthquake ground punches, survive in extreme conditions, sonic waves from thunderclaps, fast healing, break out of mystical bonds, terrifying mooks with a scream, etc.
And what Dr. Strange or a D&D Wizard can do -- teleport, summon monsters, call down lightning, shapechange, read minds, etc.
Mythic Martials should get Hulk physical magic and Aaragorn leadership magic not Dr. Strange magic as that is what keeps them "martial". (other stuff could be layered on but shouldn't be required)
They could also benefit from reliable abilities that mechanically bypass the "1 action = 1 discrete effect" and go to narrative completion.