If the essence of being a fighter is "being a trained combatant" as you say, then there are no non-combat related bits. That's like asking about the non-magic-related aspects of being a trained wizard. At most you're talking about skill proficiencies, but fundamentally the non-magic-related aspects of being e.g. Mercury Boltblaster don't originate in his being a wizard at all--he has non-magic-related aspects like crazy hand-to-hand combat skills and a close relationship with the Queen of Raelna, but those things originated in his background and martial arts training, not from his training as a wizard.
You clearly have a different understanding of what it was, and even what it
is, to be trained as a soldier today. Because there's a hell of a lot more to being a knight, samurai, Hunnic horse-archer, etc. than just making things dead. Even modern soldiers need to develop skills, connections, etc. that aren't
directly applicable to combat, but which help make "the life of a soldier" easier, simpler, or more effective.
But what really makes the idea of expendable nonmagical resources (what you call "declarative") an abomination to many people is that Vancian mundane activity is fundamentally incoherent. Let's pick a mundane activity and pretend that it's a fighter thing. Say, spotting when someone is lying. "Liar's Scent: you can tell when someone is lying to you." In what universe would it ever make any kind of sense to say "By concentrating briefly, you can tell when someone is lying to you, once per day?" What, I lose my training at detecting hinky behavior just because I talked to a different hinky guy in the market earlier today?
Vancian mundane abilities just make no sense. 5E has a few of them (like Lucky, which is kind of like being proficient in every skill). Fortunately it doesn't have a lot.
They don't have to make no sense. You just have to be careful about how you design them. That you can demonstrate that
some non-magical resources are "nonsensical," in your opinion, does not make absolutely all of them garbage. That's (part of) why I said I would need to think very carefully about the set of options for the Fighter. And, since there really are people who hate the idea of, or are not comfortable playing with, "resource-based" mechanics, a well-designed set of options should include at least two purely passive, always-on options, so that way everyone actually has some degree of choice and not a Hobson's choice.
Ok, using your definition, my first reaction here is, "Just because you personally don't like using spells doesn't mean they don't exist. So when you say there are no declarative abilities, that's not a true statement. There just aren't many that you like. Two totally different statements."
I'll let
Mike Mearls provide my defense here.
2. The Fighter Draws on Training and Experience, not Magic
Fighters master mundane tactics and weapon skills. They don’t need spells or some sort of external source of magical power to succeed. Fighters do stuff that is within the limits of mundane mortals. They don’t reverse gravity or shoot beams of energy.
??? PCs have to make saves and ability checks out of combat all the time. Almost every single skill check is out of combat, and there are plenty of spells like charm person that are used out of combat. Not to mention poison saves and trap saves. There is no question that this is a declarative ability used in non-combat.
I apologize; I should have specifically spelled out that ability checks are, generally speaking, almost purely non-combat. (There are some ability checks that can occur in combat, but they're comparatively corner cases.) Rolling a skill is not a "declarative" ability though, for exactly the same reason that "rolling an attack" is not a declarative ability--they meet the definition I gave, but only in an incredibly trivial way.
You're complaining that the fighter doesn't have any declarative abilities to do out of combat, and when shown examples, you're saying they aren't fightery enough? That seems...contradictory. Of course an out of combat skill/ability/power won't seem fightery. That's because it's being used out of fights. :\
I don't believe "Fighter" means "Absolutely Everything I Do Is About Doing Violence To Something Or Someone." Why make any class whose
definition precludes it from contributing to a character's competence in the things the designers consider fundamentally, "universally" important? (At least as much as anything can be "universal" in D&D.) That would be...utterly unbelievable to me.
The unquestionable bottom line is that the fighter has two choices above and beyond any other class to give them some pretty significant mechanics to use in the other two pillars. They will always have that extra bonus over any other class, and it's a clear defined feature of the class. The only thing WoTC did was instead of baking some of these things into the class directly, they gave you a choice to become even more of a combat bad ass, increase your ability scores, or to become more well rounded into non-combat pillars. If you (general you) choose not to use the relevant feats to achieve this but focus on becoming more combat orientated, that's not the fault of the class for not having non combat abilities. That's your choice.
And as stated, I think that's a






choice. Don't force people to choose between participating
at all in some things vs. participating
better in others, when ALL of those things you can participate in are
explicitly defined as Fundamentally Important To The Game.