It's intentionally reductionist for a reason. Mythic is magic with an artificial distinction. Much like how people argue till they are blue in the face that psionics is not and never should be classified as magic, even though psionics is a clearly supernatural. To me this feels like the kind of hair-splitting of "don't call my psionics 'magic".
I used to be a 'psionics isn't magic' guy in 2e but I got over that early in 3e... but
Batman is supposedly a peak human with no supernatural abilities. Same thing with Black Widow, iirc. Or Green Arrow. Even in a world of Gods and Monsters, they don't do anything more than a "peak human" can do. This is where I would put the limit of the "nonmagical fighter". They can do what a peak human can. If we're not making the fighter have supernatural abilities, this is my limit.
but is your limit "Something I can show batman doing in a comic/movie/cartoon" or "Something I think a human can do even if world records indicate otherwise"? If it is the former, I can get behind it. if it is the latter I can not (and of course replace batman with any non magical non supernatural/enhanced hero in fiction.)
If we are going to give them supernatural or mythic abilities, you gotta name a source. Wolverine is a mutant, Hulk was blasted with gamma radiation, Cap was infused with super-serum. If you're transcending what a normal mortal can do you gotta say how.
every hero has an origin...
we give wizards more power then gandalf ever showed (let alone ratagast) and he was a god/angel. we give wizards more power then jack vance did. we give wizards more power then merlin who was an immortal ageing backwards half demon...
if you need a 'cool origin' to get supernatural powers, then no one should be able to play wizards.
Dragons are innately "magical" creatures. They can do things fantastical because they are born fantastical. Now, if you want fighters to do fantastical things, they must either be born fantastical or somehow become fantastical.
every hero has an origin.
my buddy plays the same family line all the time... he is a human fighter who is descendent of a silver dragon (becuse way back before I was playing in 91 he played a game where his character married a silver dragon and had a family and he like playing the grand children, great grand children ect) If he was playing a spell caster he can play a sorcerer (silver dragon blood line) and get cool powers. If he wants to play a martial character there is not a class for "My origin for my warrior is that I was born fantastical"
In D&D, neither is particularly hard to do. But you gotta explain why suddenly your swordsman faster than a speeding bullete, more powerful than a lightning rail and able to leap tall towers in a single bound. Give me something.
I'm an elf, and desendent of lolth... I'm an aasimar, I'm a teifling, I'm a dragonborn, I'm a ______.... my great grand dad on my mom's side was a demi god and my great grand ma on my dad's side was directly blood of the legendary king... both powerful blood lines are in me....
I was just a farmer... nothing special, until a rock fell from the sky killing half my family, it glowed green and red and the half that didn't die in impact all got sick... except me, I was always hardy and tough, I took the metal and forged my first chain shirt and sword and went out into the world... I am now destine for greatness.
I am the 7th son of the 7th daughter of the merging of a teifling woman and an aasimar man... I have a strange power...
I fought my way up the mountain and learned my sword techniques from the old man who even though he was human but over 100 years old and still could kick my 18 year old butt...
I'm not asking for a fighter to cast spells, nor do I want him to reign in mediocrity. I just want a little more justification for why he can now do superhero mythic bullocks other than "he's 11th level now."
but it should be up to the table/people what they do and don't need... do you ask for justification for my farmboy wizard to just gain 2 6th level spells known at 11th level?