Fair enough, except that why in game-world terms would a fighter be the only one capable of being a leader and such. If your world is a feudal society then it makes perfect sense. One of the key aspects of granting land was that they were responsible for mustering an army to help defend the kingdom and fight wars. In a pseudo-medieval (and almost never feudal) society, why couldn't a wizard or some other class meet the same requirement?
On the other hand, why limit the fighter's options as well?
The thing that fighters do well, better than anybody else, is fight.
A knight or cavalier is a mounted warrior (and trained with all of the martial arts of the land - archery, polearms, swords, wrestling, even swimming). So athletics certainly makes sense, and giving them expertise for athletics skills would be a good option. Leadership abilities also make sense for them.
But many fighters aren't highly trained knights. They might just be strong and spend a lot of time in combat. So they probably wouldn't have the leadership, riding, or even the breadth of training.
Of course, some fighters are more dexterity based, so not quite the same as your standard athletic and strength-based knight.
OD&D/AD&D fighters were clearly modeled after the medieval knight concept. But that's a narrow view of what is perhaps one of the broadest classes.
I guess that's where I get stuck.
What abilities should all fighters have?; and
What abilities could a fighter have that other classes shouldn't?
I've answered this question several times on ENWorld and would direct you to my
Warrior homebrew as one example; TLDR is "camp talents."
[SBLOCK=Examples of "camp talents"]
Camp Guard (camp)
During a long rest you can keep watch without sleep, and if you are attacked you automatically awaken your allies even if you are surprised. You suffer no disadvantage from lack of sleep for a number of nights up to your Constituion modifier (minimum 1). Thereafter, you accrue exhaustion as normal.
When used during a short rest, it doubles the range at which you would spot creatures (i.e. doubling starting encounter distance).
Forced March (camp)
After a short or long rest during which you tend to journey preparations, your, your companions, and pack animals following your lead can add your proficiency bonus to their Constitution checks during overland travel (e.g. to stave off exhaustion). Additionally, you and your companions suffer no detriment from the first level of exhaustion incurred by travel conditions.
Light-Bearer (camp)
After a short or long rest during which you wrap a torch or fill a lantern with oil, while you hold the light source it burns for twice as long, has advantage to resist being snuffed out, and the radius of its light is doubled (e.g. a torch would illuminate 40 feet radius bright light, and 40 feet radius dim light beyond that).
Mentoring (camp)
During a short or long rest, you can introduce the basics of handling a specific martial weapon (e.g. longsword), a specific suit of medium or heavy armor (e.g. chain mail), or shields to one companion. That companion gains proficiency in the corresponding weapon, armor, or shields until their next short or long rest.
Mount Care (camp)
During a short rest, you can care for up to 8 mounts, allowing the mounts to spend hit dice to heal during a short rest. They regain extra hit points equal to your proficiency modifier for every hit die spent.
When used during a long rest you can procure mounts for yourself and up to 7 companions.
Under Duress (camp)
During a short or long rest, you can offer good cheer, fortifying ale, or galows humor to allow yourself and your companions to benefit from the rest even when performing more strenuous actions like overland travel at a slow pace, watching the ramparts, or casting rituals. Each character benefitting from a rest under duress loses any temporary hit points at the end of the rest as well as taking 1d6 psychic damage.
Warrior’s Guidance (camp)
During a short or long rest, you can spar and share defensive tips with your companions, granting any of your companions heeding your guidance a number of temporary hit points equal to your proficiency modifier. This represents them keeping up their guard better after your guidance.
Whet the Blade (camp)
During a short or long rest, you can use a whetstone and water to hone the edge on a number of bladed weapons equal to your proficiency modifier. A blade whetted by you grants the following:
If the blade was in good repair, it gains a +1 damage bonus on its next successful hit.
If the blade was damaged or rusty, remove the “broken” condition from the blade.
Wound Binding (camp)
During a short rest, you can expend one use of a healer’s kit to expertly bind your wounds or the wounds of a willing creature. You or that creature gains advantage on any hit dice spent to heal at the end of the short rest.
When used during a long rest, it allows you or the creature whose wounds you bind to regain 1 extra hit die (normally a long rest restores half your hit dice).[/SBLOCK]
And I fully stand behind [MENTION=40233]Salamandyr[/MENTION]'s examples of non-combat unique things fighters could do. Speaking from personal experience being taught Apache stick fighting blindfolded, awareness is absolutely the first fighting skill. Actually, in OD&D I think something like this was represented there where "Superheroes" could detect invisible creatures (or something like that, I forget the specifics).
For me, the first problem I have with the fighter class is that, unlike nearly every other edition (don't know 4e well enough to include that), the fighter was always better at hitting things than other classes.
With the proficiency bonus system, every single class has the same chance to-hit, assuming they have the same ability modifier.
I've made a lot of changes, in part because of that, and also because I don't like they way they designed the battle master. But all of my changes are almost entirely in the realm of combat abilities.
There really aren't any non-combat abilities that I can think of that all fighters should have. In part because along with rogues, I think fighters are just base "people" in the world. That could be pretty much anything.
In fact, one of the things I don't like are a couple of abilities (proficiency in thief's tools and thieves' cant) that push a rogue towards being a thief. I'd prefer they remain optional, as part of an archetype instead of the core class.
Rogues then have a niche of being quick and skillful. If fighters had expertise and Strength-based abilities similar to the core rogue, it would be more of a Strength-based person vs. Dexterity-based person. In fact, I kind of like that idea myself and might explore that a bit more.
Well, I have two answers.
First, older editions had no problem giving
all fighters two non-combat identities: The Gear Guy & The Prestige Guy. Food for thought when we start to go into the "but fighters fight, that's what they do, they fight, cause it's in their name..." spiral.
Second, in addition to the "all fighter" non-combat examples I gave, it's perfectly fine to place non-combat abilities in the fighter subclasses. In fact, I think that's a great place to put many (though not all) such abilities.