Put it another way.
So long as the fighter can never run faster than Usain Bolt, swim faster than Michael Phelps, shred better than Tony Hawk, hold his breath longer than a pearl diver, inspire people more than Martin Luther King without resorting to magic, a fighter will NEVER be mythic.
So long as the paradigm in D&D is that no matter what, no one can ever do anything that is beyond human without magic, then there is no way that a fighter can ever by mythic or legendary. You can talk about all the minutia you like. That's unfortunately the bottom line. A fighter will always be just a fighter.