Not having to do with 5e, none of the above is relevant.
On the contrary, the design philosophies that limited the initial Warlord design are extremely relevant, precisely because 5e removes them.
The question stands: should the warlord be able to demoralize someone to death? Is that a build you would support?
There's no reason for an ability like that to be off the table for a 5e class. Bards can already insult people to death - in fact, one of the most entertaining moments of an otherwise dismal season of HotDQ came from a pair of bards insulting an Urd's wings until it furled them in shame and plummeted to it's death.
I certainly wouldn't mind seeing an ability like that as part of a much larger list players could choose from. That way a player who did like the idea of a Hector-style Warlord who could destroy an enemy's will to fight without ever crossing swords with him or turn the tide of a battle with a war-cry or morale-shattering stratagem, could actually have a chance of realizing that concept. And, of course, anyone who couldn't handle the idea would have other options.
But, no, I wouldn't support a Warlord class that was hard-coded with such an ability, essentially making it some sort of morale-based controller, not anymore than I could support the warlord being represented only by a sub-class of a hard-coded multi-attack DPR 'striker' class.
There's really so much design space left open to martial concepts that the handful of non-casting classes haven't explored. All the formal, traditional, and imputed roles except Striker. Morale-based effects. Followers. Formation-based maneuvers. Modelling IC tactics & strategy as distinct from (or dovetailing with) system-mastery-optimal tactics & 'player skill' metagame strategies. The 5e PH focused so heavily on casters that there's just a lot of room for expansion and improvement elsewhere.
True.
But we still have to be able to evaluate the individual mechanics and elements of the class. We have to look at what worked and what didn't.
We do. I ran 4e for it's full run and played a number of Warlords in all three Tiers, and and can conclusively, and truthfully state that the hp-restoration mechanics of that class worked very well, indeed. You and Epiphet, OTOH, are unqualified to make any such judgement.
Shutting down discussion of a mechanics, any mechanic, with the edition war card is not conducive to the discussion.
Shutting down discussion of the /mechanics/ is what the edition-war talking points being recycled
do. They're invalid objections, repeated ad nauseum, no matter how many times they're refuted, turning any attempt at a worthwhile discussion into an endless loop of recriminations.
If the concerns were truly irrelevant, why do they keep coming up?
They are irrelevant in the context of 5e. They were /invalid/ before, and still are. But the irrelevance of a philosophical or personal-taste/opinion objection to a mechanic in 5e is obvious: Any forthcoming Warlord, by definition, will not be part of the Standard Game, it will be strictly opt-in. There's no foundation for excluding a mechanic just because a particular sub-set of the community wants to deprive everyone of an otherwise excellent mechanic and extremely interesting and enjoyable class. Not even the tenuous, petulant cry that you "shouldn't have to ban" the stuff you don't like. Irrelevant.
Any hypothetical Warlord would, perforce, be a modular addition, you'd have to opt-in, you could continue to play the Basic or Standard or even Advanced game with modules of your choice, without ever being afflicted with the presence of a worthwhile martial class.
First, a Warlord doesn't heal anybody; the Warlord's words initiate a response where someone essentially heals them self - allows their body to regain homeostasis. The Warlord is just the initiator and catalyst, not the one doing the healing... Hit Points do equate to health in this situation. Actual recovery from damage occurs. No, injuries themselves do not suddenly knit together. What occurs is that homeostasis is re-established, and loss of homeostasis is damage.
That's an interesting way of looking at it, and really goes far beyond the standards of fantasy tropes that should, alone, be more than sufficient.
Three, while one can be inspired to recover, and there are even real life examples of this, I know of no examples of the opposite - at least not of an immediate and explicit nature, which is what it seems to me you're describing.
Nod. Examples from RL, such as a victim of a 'curse' giving up on life and wasting away, do take a while to manifest. A sudden morale failure certainly could be immediately fatal in combat, but the proximate cause of that fatality would still be a physical injury, just one sustained as the result of giving up or panicking in the midst of battle. In ancients and medieval battles, for instance, the greatest casualties were generally inflicted upon the losing side after their morale broke.
A very abstract way of modeling that could be simple hp damage or 'psychic damage' or even a new 'morale' damage type (though that hardly seems different enough to be worth it, you never know how much symantics might matter). To model that less abstractly, the Warlord could be given a 'morale attack' that imposes a condition, reduces AC or saves, causes the next attack that hits to be a critical, or quite a lot of other things, including inflicting damage, but not to 0, or with enemy fleeing at 0 or whatever.
5e is really pretty wide-open when it comes to available/hypothetical mechanics.