(The name of the class on the other hand, I can't tolerate.)
It's funny, because it's the best name they've ever come up with. Marshal is terrible - it has two possible meanings, to Europeans, it's a general, so locks in military rank and all that implies, to Americans, it's a law-enforcement officer, totally inappropriate. Most other alternatives are military ranks, or otherwise imply rank (like Captain, which can also refer to the civilian commander of of ship) - too narrow in what they imply, and in-use, today, so bringing with them modern anachronisms. Warlord both has a strong fantasy sound to it, and has no implication of military rank. A Warlord can lead merely by example, by formal authority such as military rank, by acclaim, by threat, etc... And, yes, a Warlord could be an aweful person like a tribal strongman or rapacious orc chieftain - just as a Sorcerer or Wizard is often a villain in genre (or RL, where 'Sorcerers' are charlatans who exploit the superstitious).
I'm not really seeing anything substantive that is missing from the warlord's schtick in the offerings we currently have. Unless I don't know how to read the 4e PHB, the warlord's main things were healing and buffing allies and granting them actions.
The Rally maneuver heals allies (temp hit points).and the Inspiring Leader feat buffs your entire party's hit points.
Not healing. Healing can stand a fallen ally. Temps are a very appropriate buff for the Warlord, and he had a lot of things to grant them, but they're not healing. They don't even fit the name, which implies recovery. If Inspiring Leader were hp-recovery, it'd only make thing worse, since it'd be giving the Warlord's fairly unique schtick to anyone who wanted it.
The Distracting Strike maneuver buffs an ally's attack,
The Maneuvering Attack maneuver allows you to grant an ally movement, and the Commander's Strike maneuver lets you grant an ally an attack.
CS dice are just too few, and these effects to minor. You can do one of these a couple of times between rests, and their impact is minor. Commander's Strike, Wolf Pack Tactics, and Furious Smash did those three things in 4e, and they were at wills, and they didn't obviate the need for the hundreds of other maneuvers the class had to choose from.
Conceptually, I can't see anything else needed to fit the archetype than a Battle Master fighter taking those 4 maneuvers and that feat.
Would you think a Rogue with expertise in arcana who could learn 4 cantrips and take a Ritual Caster feat would be an adequate replacement for the Wizard, Sorcerer, and Warlock? That's how far your Battlemaster is from being a Warlord.
Would the demand for a warlord feel met by a list of new maneuvers to provide additional options? I mean, that could be done, but even then it seems like the current maneuvers more or less have the bases covered. There are only so many things to mechanically do in 5e combat.
That is another issue. 5e obviates some potential maneuvers by removing a lot of depth from combat in the name of speeding it up. That just means any maneuvers or resources modeling tactics/strategy/etc need to be yet more abstract.
Battlemaster-style manuevers are hopelessly hobbled by the need too keep the class balanced in spite Fighter's very potent, high-DPR, easily-breakable, multiple attacks. A Warlord class wouldn't be a DPR monster, and probably wouldn't make multiple attacks (at least, not himself, every round - possibly he'd have some options that allow them sometimes).
Perhaps a new Fighting Style that is only half about fighting and half about warlording somehow (take the Mariner style for precedent).
No style, sub-class, feat or background takes away from a class the way you'd need to take away from the fighter to make room for the kinds of abilities needed. The fighter's core, before sub-class, is so focused on high single-target DPR, that it's not given any meaningful features to use in Interaction or Exploration, for instance - no other class is so invested in a single function as to require such extreme measures to balance.
I mean, really, I think it may be an emotional appeal more than a logical appeal.
Actually, it's the objection to the warlord that's emotional. The reaction to the name. The reaction to non-magical hp restoration. The lingering, irrational, spite still directed at 4e.
I get it. I wanted an assassin base class. Why? Because they felt different than just a type of rogue.
It was a Thief 'sub class' from the beginning, and it's abilities have never been that different from the fighter. It's like the Illlusionist, that way.
Now, if you wanted a 4e Assassin, with Shrouds, no, the Rogue sub-class wouldn't cut it. But you'd be talking a de-facto caster, or at last magic-using class of somekind.
The point is that assassin is covered by rogue in the level of detail and abstraction that fits 5e. Warlord seems to be covered by the Battle Master in a similar level of 5e-appropriate detail.
It's really, really not. The assassin started as a Thief sub-class, has been nothing more than a Kit at times, and has always just done some of what a thief does, plus disguise (which thieves/rogues have been able to do for a while) and death attack. The 5e Assassin does most of what a thief does, plus death attack. It works because they are very similar. The same is not true of the Warlord, which has always been a full class, and which does a great many things the fighter has never been able to, and has never had the uber-DPR of the 2e figther that is the template for the 5e fighter.
I can understand not being happy with a favored class being just a sub-build of a subclass (those 4 maneuvers are the only ones that have anything to do with being a warlord). But I can't really see how a warlord class could be elegantly introduced to the 5e class design space. It has to pretty much either just be a few more maneuver or feat options, or it has to add an entirely new set of systems to 5e, and risk throwing off the way the various elements of the game cohere.
The 'coherence' of 5e is a non-issue, balance was never a goal, and they DM imposes as much balance or coherence as he feels his campaign needs.
Design space for new martial classes is wide open. Consider the existing all-martial classes: there are none. Now, consider the few exclusively martial sub-classes: The Barbarian (high DPR), the Champion (high DPR), the Battlemaster (high DPR), the Thief (high DPR, skills) and the Assassin (high DPR, skills).
So, what's left: everything but high DPR and traditional 'thief' skills (stealth, thieves tools, etc). That is a tremendous amount of design space, including the Leader, Defender, and Controller formal roles from 4e.
The Warlord was not a high DPR class (it could goose other class's DPR, but it wasn't, one, itself), didn't really impinge on the Thief's traditional skill bailiwick, and was a Leader (secondary defender or, maybe controller, if you squinted).
There is not only room for the Warlord, but an expansive Void where the 4e Fighter and Warlord should be.
Would the Warlord work as a nonmagical Paladin archetype?
No, but a non-magical Paladin archetype could be pretty darn awesome! I've had one percolating, but haven't really tried to bang it into shape. Called "Oath of Fealty." The idea is a knight as committed and honorable as a Paladin, but committed to a temporal power or cause, like a King or order or nation.
