On a less tongue in cheek note, there's that use of the word "mundane" again. I hate that mundane gets applied to non caster PCs. They are not "mundane" they simply have a different focus. Especially in a game where everyone starts at the same level (often 1st) and then journeys from there. The D&D zero to hero journey applies to martials AND casters not just martials.
I'm using the word accurately, given the context. You're thinking of it as a synonym for "banal;" I'm using it as an antonym to "supernatural." And that's the first and last time I speak on that here. I'm not getting dragged into a definition war again. Of course if you're saying that pure martial classes like the fighter
should be supernatural, then I guess I just disagree with that completely.
You are missing the core problem. The Fighter's 'thing' is 'Attack for damage and nothing else' and 'Attack perhaps a second time for damage and nothing else'.
And there's room to improve on that without making them supernatural. Most people here that are against making fighters go demi-god as a matter of course aren't against improvements. It's just that many of us think that there's only so far you can push pure martial classes before they stop being purely martial (and we think that would be bad).
But personally, I think there's plenty that can be done while keeping the source of improvements skill based rather than raw power based. But a lot of it depends on fixing the underlying math so that depleting HP isn't frequently the most efficient action. You could also use rider effects to add different actions on top of your attack, save-or-die actions, and so on.
The key to making it work for people who don't want superhero martials is to frame both the narrative and the mechanics in a way that is clearly not magic. For instance, using D&D spell economy for martial actions is a dealbreaker for me. But you have to have
some limiting factor or you have to limit the strength of the abilities. So maybe give a lot of potential actions, but give them diminishing returns with repeated use within a fight. Less effect or harder to pull off each time because once the enemy sees it, they're more likely to counter it the next time. You could even say that only happens with opponents of at least human levels of intelligence, letting martial characters really shine against opponents that can't use complex tactics. Then you give them an ever expanding toolkit as they level, meaning that they never really run out tricks; they just have to change things up and decide when best to use what ability.
And then, again, I'm
also for lowering the "magic" ceiling so that it doesn't take
quite so much to get magic and martial to find a middle ground. Mostly by treating powerful magic the same way we treat powerful magic items.