It's not a "double standard" It's a different standard.
A different standard applied to equivalent things is a double-standard, by definition. Classes (and sub-classes) are equivalent choices in D&D. Not identical, but you get to choose a class. It's not a case of some classes cost 5 build points and others cost 10. They're equivalent player choices.
So, yes, holding some (sub-) classes to one standard and others to a different standard /is/ a double standard, with all that implies.
You don't need to define what a martial character is capable of because it's apparent: you can do what is reasonably physically possible based on a lifetime of living in the real world.
There's the double-standard again. You hold one concept to the standard of the real world, the other you do not even hold to the standard of the fantasy genre it's derived from. Heroic character in fiction do not adhere to what is reasonably physical possible based on mundane experience in the real world.
D&D purports to draw inspiration from a range of genres, most of them very much heroic sub-genres, from high fantasy to S&S and even a little science-fantasy and science-fiction and action thrown in. To hold some characters (barely) to the standard of tropes in heroic genres, and others to the standards of RL is a painfully obvious, clearly inappropriate double-standard.
And, while 5e has yet to really take full advantage of it, there are signs it's not as down on martial characters as you'd like it to be. Second Wind - hit points in general, really - and Action Surge and a few of the BMs maneuvers model a few of the many things you find in genre that don't quite squeeze under the bar set by RL.
You do need to define what magic does because it's not as automatically apparent.
You need to define what each PC is able to do, because no matter how apparent it may seem to one player (or the DM), it might seem equally apparent to another that it would do no such thing. Doesn't matter if it's magic, psionics, martial skill or something else.
In the same way a modern RPG doesn't need to define what a gun does
In Hero, a gun is an RKAp, in 1st Ed GURPS, a gun did 'bludgeoning' damage (so that they could punch through armor), in later eds that was changed to a different damage type that was even better at penetrating armor, in Top Secret a gun had a PWV, range mod, & 'speed.' Modern RPGs absolutely define what modern weapons can do in them, because everyone has to be on the same page when the shooting starts. And, for that matter, because what a gun can do varies based on genre and tone. In Hero System, a superhero can bounce bullets off his chest, while a tough heroic character might take a bullet wound, even several, and keep going - he might even be mortally wounded & dying, but still able to act - or he might be knocked unconscious by a wildly improbable 'crease' to the head and wake up later with little more than a scratch. In Top Secret, a gun could kill you quite easily, but you'd go unconscious first (and probably burn through some Fortune points before then).
You can't use your foot to lop a weapon on the ground into your hand without the Kick-Up feat. Suddenly, every other martial character everywhere loses the power to dramatically flip a dropped weapon into their ready hand with an Acrobatics check, negating the Attack of Opportunity. And instead, people have take a feat (which is limited to swashbucklers IIRC) to do so.
Nod. I've seen that phenomenon with skills, too, in many systems. Adding to the list of skills doesn't let characters do more, it 'creates incompetence' in everyone who doesn't have the skill, when, before, the tasks it covered might have fallen under one or more other skills, or been deemed not to require a skill. And I have noticed the issue with some feats in 3e, for instance. It's a thorny problem with skills, because skills tend to model training/competence that's consistent and always available, as opposed to wild heroics or extraordinary abilities, for which its less of an issue (since not everyone in the world is going to be extraordinary or heroic, obviously, and PCs do tend to be differentiated in their abilities).
I do a fair bit of design, but thinking of many non-limiting martial utilities, especially at-will ones, is tricky. Ones equivalent to a cantrip in power.
What would you suggest?
I don't purport to design, at all - at best, I tinker. But, I would suggest not needlessly constraining the design space open to such abilities.
For instance, don't think that a limited-use ability implies that the fluff that typically goes with it is otherwise impossible. Expend a resource (Inspiration, CS die, whatever) and so something wildly difficult and improbable, once. Or, make a check to try to do it and try to hit that DC 30. That kind of thing.