pemerton, If you are arguing that 5e is unable to portray Boromir's death scene from The Fellowship of the Ring, I agree. It was why HP recovery from Hit Dice and full HP recovery from 8 hours of rest was a bad idea to include. They probably should have made it an optional rule.
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A Warlord class would take that mechanic and make it front and center.
I think that there are two features of 5e that get in the way. One is very easily tweaked. The other is a bit more baked in, but probably not so fully that it can't be tweaked too.
The easy one: changing the ingame time required for recovery. This is as easy in 5e as in 4e. (For balance reasons, everything else built around that schedule needs to change too, not just hp recovery - but for a Tolkienesque feel, having spells and the like return on a weekly or monthly cycle rather than a daily one is a feature, not a bug - it slows the whole pace of the game down for that more languid, "roll of years" feel.)
The trickier one involves what happens at zero hit points. First, you have to get rid of healer's kits and have to stop treating stabilisation as 6 seconds of medical treatment. This completely ruins the verisimilitude of a game that is meant to involve more-or-less mediaeval technology, by bringing in sci-fi style "medipacks". Making stabilisation a matter of inspriation, and of having a friend persuade the dying person not to go into the light, brings the game closer to the classic fantasy tropes and feel.
Second, you have to slow down the dying process, and allow for dying words. That doesn't mean you have to slow down death saves, but it means that when the final death save is failed, the character is dying but not yet dead. This is how, for instance, you can have Boromir speak his dying words to Aragorn; or have Eowyn carried from the field of battle and then (with the application of suitable magic and healing skill and the love of Faramir) recover.
This change then makes room for a third: healing skill, plus inspirational abilities, are used not to apply implausible field medicine but to actual help people recover in hospices and the like, over time. This also allows for an inspirational rather than cleric-style healer to use "Raise Dead" effects: they don't literally bring the dead back to life, but rather are able to restore hope to those who have failed all their death saves, and so who would - without such intervention - die over a period of time.
And this sneaks in every time. In order to be an inspirational leader you require all other characters to be inspired by your character and they must recognize him as a leader.*
Honestly this might be a case where the Warlord would just require buy-in from the rest of the group in a manner similar to how the old-school Lawful Good Paladins had to be approved by the rest of the group so they didn't end up killing each other. If the rest of the group agrees to let your character be the leader, there is no problem.
*And what if there are two "inspirational leaders" in the group? How does that work? You never see a modern military group with two leaders. And for good reason.
I think you are giving the word "leader" a lot of weight, probably more than is warranted.
First, on the issue of two leaders: the Fellowship had two leaders (Aragorn and Gandalf), and in Sam's case there was a third (Frodo), and survived.
More generally, leadership in this context is not about command authority; it's about the power of personality. In the context of D&D play, I've never heard any suggestion that when one person is playing the warlord, s/he is entitled (in character) to tell the other players what to do (in character). The capacity of the warlord PC to lead those other characters is already mechanically built into the class - we know that when the warlord character tells another character that it's not yet time to die the other character listens, because the player of the warlord declares an action that restores hit points to the dying character. The player of the dying character doesn't have to make any choices or follow anyone's instructions.
If the group doesn't like the flavour of this then it mightn't work. I don't see how that's any different to a player who doesn't like the idea that his/her PC is inspired by the bard's song, or is blessed by the cleric's pagan god, or anything else of that sort.
Maybe, across the D&D cohort as a whole, the idea that one's PC might be inspired by another's PC is more controversial that that one's PC who is devoted to god X might receive blessings from another PC who worships god Y. It's not anything that's ever caused an issue in my group, though.
