I agree that self-healing or self-generated damage mitigation are not the same as the Warlords inspirational healing. You're right, they do all emulate different tropes.
The mechanic needs to be an external, inspirational one (as you posit), and not a self-generated or self-possessed resource. However, I do not believe (as some stubbornly stick to) that this requires a unique and seperate class. I think seperating these abilities into something any character can take allows for building a straight-up, 4E Warlord emulation, and allows others to also add such Warlord characteristics to their non-Warlord characters.
My main reason for thinking of it as happening at (roughly speaking) the class level rather than the feat level is that, if it happens only at the feat level, it's likely not to be robust enough (in terms of reliability and effect) to sit nicely against a cleric.
(Burning Wheel doesn't have this problem, because it's a classless system.)
That's not an argument on its own for a
separate class, though - I'll come back to that in replying to KM.
inspirational healing and the warlord as a character class aren't necessarily linked to me. You don't need the inspirational healing to be a charismatic tactical commander, and you don't necessarily think of inspirational healing when you think of a charismatic, tactical commander. And they can still go together, though they needn't.
A charismatic
tactical commander isn't necessarily about healing. But someone like Aragorn or Faramir or Arthur is not primarily a tactical commander. They are
inspiring commanders. They restore hope and engender resolution.
If D&D had very robust morale effects for PCs, they could operate upon that aspect of the game (and paladins would fit into that model, too). As it is, though, D&D does
not have robust morale effects for PCs: PCs are only affected by fear when it's overtly magical (and hence mind-controlling) in nature. Hence, the only domain of combat capability for inspirational leaders to work on, at least that I can see, is hit points.
Hence the reason why the warlord sits alongside the (STR-)cleric or the paladin: all are combatants who also inspire and restore resolve, courage and will in those whom they lead. And the model for this is hit point restoration.
Basically, three kinds of vampire.
Meaning, there's a lot of different mechanics that can get at the idea.
Fighter who can share his bonus die with allies? Bard (inspiring song) with a soldier background? Ninja with a certain specialty that lets it spend actions for others (4e warlord mechanics divorced from the class)? Rogue with a high Charisma (just has high skill checks)? Paladin who establishes a war-temple and attracts an armada (some sort of domain management system)?
I'm a fan of multiple mechanical models for most things.
Sure, but before we get to three kinds of vampire let's get at least one up and running.
Aragorn is (to me) pretty clearly not a ninja, nor a rogue. Despite the tendency of all Tolkien protagonists to recite poetry at the drop of a hat, I don't think he's a bard either - nor is Faramir or Arthur, in my view. The D&D bard is too much it's own thing these days, and is not associated primarily with being a battle captain.
Of your options, that leaves the paladin - which I already canvassed as occupying the same archetypical space, but in the D&D context being overtly magical - and the fighter.
If we look at the fighter for a non-magical option, we have to consider what can be traded off to create adequate room for an inspiring martial leader who will be capable of occupying something like the same mechanical space in the game as the cleric does. In 4e, the fighter has quite a lot to trade off: armour proficiency, marking and the associated combat challenge, a very meaningful +1 to hit, and better hit points and surges.
In D&Dnext, I don't have enough of a sense yet of how the classes are built to know what the scope is for trade offs. But hit points, at least, seem to be defined at the class level. The fighter doesn't have anything quite like marking to trade off. Attack bonuses seem to be built in at the class level. So really, we would be talking about trading off perhaps some proficiencies (the cleric builds provide a precedent for that) and the expertise dice options.
The current options don't strike me as going very deep. Strike Command seems somewhat weak, especially as a fighter is a pretty reliable hitter and so is likely to be better off going with deep wound or, if a frontline combatant, the perhaps overpowered (in compared to the others) shield slam.
Warning Shout looks more useful than Strike Command - permitting a buff of AC to lower-AC PCs - but doesn't on its own capture the spirit of the romantic battle captain, nor substitute for healing. Bolster Allies is comparable in this respect to Warning Shout, I think.
Oddly enough, Attack Orders looks like the best of the "warlord-y" abilities, because it lets the fighter buff attack rolls carrying heavy payloads (eg the wizard's Ray of Enfeeblement). But that's still not giving us the romantic battle captain archetype.