The common argument for the "martials" in this debate is that past a certain level point, they want to see that gap shrink. Aka high level martials should be doing "the impossible", not in the same way as casters, but in a way that a low level person would watch and go "I can't believe it".
Most people are fine with the low level martial being grounded by physics and the wizard every once in a while bending the rules of reality a bit. Because the gap isn't that large and the number of times the wizard can do it is relatively small. But past a certain point, the bending of reality gets pretty intense, and the martial is still grounded by physics. The camp that wants martials to close the gap basically want to remove that grounding at a certain point, and allow martials to start doing some reality bending "impossible things"
This is right. With a couple adds:
* this is assuming that spellcasting remains the same. a lot of folks wouldn't mind spellcasting being reigned in and thus less of of a need for martials to get so mythical at high levels to begin with. but for many this is a ship has sailed, so let's figure out martials within this context.
* a common trait of those arguing for "mythic martials" seems to be that they are pretty flexible. They don't mind if the current Fighter/Champion remains in the game. They just want other options that close this gap. They don't care if it's called Fighter or not. They are ok with some kind of power source to explain why it's possble, etc. They are fine with several flavors so people can be happy -- mundane guy + class magic items, mythic power source person, keep the current Fighter, etc. Many are ok with it being an optional class(es) in seperate books as well.
What I can never figure out is why some people are so opposed to adding this option to D&D? As long as the new class is equal to or less powerful and versatile than the current Wizard, what's the big deal?
Even if you are ok with the current Fighter, does it hurt you somehow to have additional options?