I'm A Banana
Potassium-Rich
Some people are completely intolerant of Fighters that deviate from the OD&D -> PF paradigm of fighter-as-fodder, demand a game that has class-itis, or will nit-pick every non-magical effect in a system to death.
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The question is what kind of subset is the Fighter? To some people the Fighter must (no matter if they are the one playing the Fighter or the one playing another character at the same table with a Fighter) be the big-dumb-jock who has heavy armor, big weapons, and deals in nothing but hit points or it's BadWrongFun and "Not Real D&D."
I do not think this opinion is as widespread as you seem to fear it is, but since it isn't either of ours, I'm not sure it matters that someone somewhere might behave like that.
In D&DNext the Successful Player Character is the archetype of "guy who is awesome at combat."
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The Fighter should be the master of arms, the best at any sort of direct application of weapons - bows, swords, axes, hammers, fists, lances, spears, fists, whatever. He must have access to all forms of armor and shields as well as a lot of hit-points to endure a prolonged or especially heated melee.
Should the Warlord be a Warrior? Yes.
Must the Warlord be the ultimate master of arms? No.
Must the Warlord be the hardiest and stoutest on the field? No.
Therefore, a Warlord need not be a Fighter any more than a Monk or a Barbarian need be.
I'm not yet convinced of your first statement, and I think if the game turns out like that, we're going to have a lot of disappointed players.
As for the rest of it, I think "guy who is good at using equipment" is also a subset of "guy who is good at combat." To me, the Fighter is the latter, and one example of this is that they can use equipment well and another example of this is that they can use their party members well, and maybe one fighter will learn 1,000 different kinds of moves with his favorite sword and another fighter will learn 1,000 different kinds of weapons and another fighter will learn 1,000 different strategic plans of attack, and another fighter will learn a few moves with his favorite sword, a few extra weapons and shields, and also a handful of strategic abilities to help improve her allies.
The common denominator of all these things is "combat." That's the Fighter's bailiwick: fightin'. It's right there in the name.
Monks, barbarians, rangers, whatever....they might be capable in combat, but they are not about combat. Monks are about enlightenment and mysticism. Barbarians are about losing control and being dangerously unpredictable. Rangers are about knowledge and intimacy with the wilderness they live in. Paladins are about crusading and justice and nobility and probably horses.
A warlord, as a "guy who is a tactical strategist," is still a guy who is about combat.
It's the same way that a sorcerer in most 3e games was functionally, "guy who casts more spells," thus being a guy who is still about magic spells, and thus being a good candidate to be a subset of some Mage class (the guy who is about spells) in NEXT, rather than its own class.
Or the same way that the assassin in play is really "the guy who sneaks up and stabs people," thus being a guy who is about stealth and sneaking, and a good candidate to be a subset of Rogue (the guy who is about sneaking and stabbing) in NEXT, rather than its own class.
In my view, it kind of weakens the fighter if you say that they can't be the guy who is the strategic genius, and that if you want a strategic genius, you have to play some other kind of class, not a fighter. Fighters in my mind are not only about some limited space in combat (like "weapon" or like "melee,"), they are about the whole bag.