I was going to reply something along this lines. I don't care what the label was, martial powers could only be explained as supernatural.
Obviously, you could, as the DM, remove a power or change it's keywords if you found it didn't fit your campaign, and, as a player, you could always change fluff to fit your character concept, or simply not choose a power that didn't fit it.
But, the 4e fighter & it's powers were explicitly not magical, nor supernatural, though sometimes super-human. Just as the Monk's ki, in 5e, is explicitly magical, even though it's used to some do things that aren't necessarily superntural (many Open-Hand uses) as well as things that clearly are (by the other two 'Ways').
Take the lowly "Come and Get It". You forced movement, can only do it every once in a while and you get to wack everyone.
Nod. It's the kind of thing that happens in the action genre all the time. The minions are no match for the hero, but they come at him one-at-a-time to be cut down, anyway. Why didn't they attack him all at once and beat him down in 2 seconds flat, or keep their distance and pepper him with missile fire? Because that'd be a sucky action scene.
Yeah, I know you can say it's just yelling at people and pissing them off, but how do you insult an wolf?
You meet it's gaze, they're like dogs that way, it's a challenge.
Really, the dumber the monster, the more predictable and easy it's going to be to manipulate tactically. A golem or ooze, for instance, C&GI and other 'trick'-based maneuvers should 'realistically' be at-will vs things like that.
No, there's nothing supernatural, or even terribly unrealistic, about goading, tricking, or maneuvering enemies into a tactical mistake (and not being able to do so constantly, for that matter) - nor, on the other extreme, is there anything supernatural, about a player pushing a genre-conformance button to 'make' enemies do something (another, willfully 'dissociative' way of imagining C&GI as non-supernatural, if it works for you).
But, ultimately, it was up to the player to choose and describe his powers in ways that fit his character concept, including any personal bars he had for realism or fantasy tropes.
In 5e, the magical/superntural status of various class abilities is mostly explicit, and it's up to the DM to change them, if he likes.
Yes, champion fighters in 5E push the boundaries of what is physically possible, but I've also seen videos of archers who can fire more arrows in a short period of time than I would have though physically possible .
Every fighter heals itself instantly with Second Wind, or suddenly doubles his speed with Action Surge, each - separately - only once/rest. CS dice are similarly guilty. It's no different in nature, just fewer in number - and thus not so nearly-balanced with the supernatural powers of other classes.
Yeah, about all I see that they could do to address these things without making the game less useful to huge groups of people is to make the game a bit more flexible and modular, but even then you have to consider that one of the biggest criticisms of 5e is that it isn't focused and defined enough.
Adding options, especially in one-off supplements not necessarily meant to be combined with other one-off supplements can address both issues: it can add options for types of characters and campaigns the game doesn't handle well, as it is - /and/ when applied by itself, such a supplement can make the game more focused and defined.