Because that would take more effort.It's a new class, so why not a new background? In either case, given that I take "warlord" as looking less like a refined gentleman and more of a battlefield commander, I would have gone with outlander. Even soldier is fitting.
I was following the PHB, which suggested a background.See, the thing with 5e classes is, even if you have to tilt your head and squint a bit...a well-designed class should be able take on/handle any background. That's just a matter of backstory for the player to work out.
Regardless of the HP amount, it requires that other players sacrifice their own class bonus actions while also requiring the warlord to maintain the ability. In terms of the action economy of the game, it gimps everyone. No one would use it. If no one uses it in lieu of their own class-oriented bonus actions, there's no reason for the warlord to use one of their own class features. Ergo, why bother playing the warlord?
Because people want a baseline non-magical support. I can't spell it out any clearer than that. For you it has to be magical. I get it. You clearly don't. But it does not sound as if warlord archetype was ever for you anyway.
But for actual advocates of the warlord and what it represents, it has to be non-magical at its core. For you it has to be magical. Great. But that's not what most warlord players want. Sure we could make a magical warlord sub-class that would appease your magically-inclined sensibilities, but that should not be the expectation of the core class. It would feel like a complete betrayal of the warlord concept.
I have a novel idea. Let's fluff the core fighter, barbarian, and rogue as magical, including the battlemaster and champion. I'm now of the opinion that there is no way they can achieve these extraordinary things without magic.
Seems pretty clunky, and gives even less agency to the cheerleader.So how's this: "Rallying Cry: the (insert class name) uses an Action to begin shouting a repetitive martial cheer. Allies who can hear the (insert class name) can use their bonus Action to join in the cheer. All who do so gain (some amount of) temporary Hit Points. On subsequent rounds the (insert class name) can maintain the Rallying Cry using a bonus action (requires Concentration), and allies can continue to benefit by using their own bonus actions."
Seems pretty clunky, and gives even less agency to the cheerleader.
"I choose to make a bonus, you choose to recive it, you choose how to spend it".
Heck, by those rules, an enemy can simply join in the chant.
I mean, every other support at least get's to choose where there bonus goes, if not how it's used.
After you give a buff, and it's no longer your buff, it's their buff.I also think we may be using agency slightly differently. I'm talking about agency of thought & action, with the outcome being dependent on other factors. You may be using agency to mean "ability to accomplish desired goal".
Possibly a chanter class.
I was more picturing two warriors getting in each other's faces, yelling "WASSSSSUP!!!!!", head-butting, then turning around and scoring crits on the Frost Giants. Not Gregorian Monks droning.![]()
So a "Bro" class then?
Because that would take more effort.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.