What it will take to make the warlord is the ability to organise a non-magical party to function without significantly reduced capacity. A significant part of this is something with the utility of spike healing.
I think we might be able to work with that as a thesis, yes?
And I note that it doesn't involve spike healing as a class ability, or any reference to a need for a class at all. I'll take this as agreement that you don't necessarily need a warlord
class to get the effects you want. Whether or not the effect is a class ability is open to discussion, at least.
If you mean that the Fighter can get Inspiring Word in place of most uses of expertise dice and the rogue can in place of sneak attack I do not consider that meaningfully different from a unique class feature. It'll be ... interesting ... to balance. But that's details.
That works. But I think you're still tethered to this idea of it being a class ability too intimately.
Lets take something no one is seriously proposing, but that meets your criteria above. I've been thinking about equipment recently, so what if it was, say, a mundane item, a piece of gear only as character-defining as a greatsword or heavy armor or a shield might be.
Battle Standard (xxx gp): When this item is worn, it provides hope and resolve to all who fight in its presence. This may take the form of a flag, a pennant, a medal, an insignia, or even a particular battle cry any other rallying point you can imagine. If it isn't a specific item, the GP represents the training and practice that goes into having the capacity. A bearer of a battle standard can (insert favored spike healing rules here, copypasta'd from the identical cleric ability).
That would allow a player to organize a non-magical party who would benefit from spike healing and so be mechanically and psychologically indistinguishable from a cleric doing the same thing magically. It would not be a class choice, it would be a choice of equipment, like choosing to wear plate mail.
I imagine it fails to meet some un-stated threshold of yours for "working," probably for a litany of reasons. I've got a few problems with it myself, and that's the point. Lets silo the reasons that are about the specific balance of the item (slots or gp value or whatever) and dig down on the most significant way that fails to meet your thesis above conceptually, to see how we can refine that thesis to more accurately represent your actual position. Presume the item is properly balanced with other items and the action economy and whatever (ie, that it is a valid item): in what way would it not "work" conceptually?
If you mean that everyone gets Inspiring Word, that would have a very bad impact on the game. It means any smart NPC is going to confirm kills with a coup de grace. And it's going to render focus fire a very weak tactic.
I don't follow your logic, but that's irrelevant. This would presumably happen in a 4e party full of warlords (or other leaders), too. Or, hell, a 4e party full of war
forged.
But we can fix what may have been problems in 4e, so lets put in a hurdle. Instead of everyone automatically getting inspiring word, we have a feat that lets you use the equivalent of inspiring word, but limited to characters with a Cha of 13+. Now it requires an investment in terms of ability score opportunity cost and a feat: likely only one member of the party is going to opt in, and occasionally you might have two or three, but you're not realistically going to have them ALL do it (hypothetically possible, though, still).
This also allows you to have a party that isn't magical that has spike healing exactly equivalent to a cleric's spike healing. It still does not require a class. Does this also fail to meet some un-stated threshold of "working?"