I think that's were my idea came from it. That in old school d&d, fighters were the ones that became lords and raised a small army.
It's been interesting to see how many different views peoppe possess of what the fighter is to them, which I think speaks well to your comment on a lack of identity.
Your idea is interesting. Whereas in old school D&D, fighters became nobles ruling over others, in your version the fighter has a "common touch" making it easier for them to make friends & influence people across all strata of society.
Regardless of what your answer is to the question
"What is the fighter's identity?", I think the right place for the rules to answer that is predominantly in the subclass.
There are two reasons to place the weight of the fighter's identity in the subclass, as opposed to the heart of the class itself. First, it allows the class to be versatile and adapt to multiple ideas of what being a "fighter" means. Second, it places the additional features at 3rd level, thus avoiding further weighting the early levels when players are most likely to "dip" multiclass into fighter for Action Surge builds.
If you look at class design generally, you'll notice that the Fighter and the Rogue are alone in only having one feature at 2nd level. Every other class gets 2 or 3 things at 2nd level. Same goes for Fighter at 5th level as compared to the Barbarian, Paladin, and Ranger – Fighter only gets Extra Attack, the others all get other coolness on top of Extra Attack. These are "openings" for design additions to the class.
This comes down to personal views, but I think the more the rules can discourage "dip" multiclassing in general, and
especially for the fighter class, the better. Because the fighter's identity has been eroded away over the editions, and its special features parceled out to other classes. Obviously, people who enjoyed 3e's approach to the fighter & multiclassing (and by extension PF's approach), and the latest UA "multiclassing lite" feats, would disagree with me here.