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?
That still doesn't make sense. What if the missing text were "twice your maximum HP"? Who
wouldn't sacrifice one action from the healer, and a bonus action from each character who needed healing, for that much healing? Not that I'm suggesting it should be that much, but clearly there is some value at which it becomes an interesting/hard decision. "Gosh I hate to give up my bonus action....but that's a bunch of HP."
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.
Actually, a few people (Bawylie, mellored) have convinced me that a "master of tactics" could be a fun and useful class. And throwing some healing in there is a good idea. I don't think questioning the necessity of one aspect of the fluff, with nothing to do with mechanics, is doubting the whole archetype.
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'll try to make an analogy: if we were debating the Druid and I kept arguing, without budging an inch, that Druids should only be able to use non-metallic weapons, would that detail seem like a deal-breaker to you? "Dude, if you don't like metal weapons, don't use them in your game.
It doesn't change anything." (Which is exactly the approach I'll take if the Warlord makes it in: I'll pretend the healing is magic.) I'm just trying to understand why non-metallic weapons, or non-magical healing, are so freakin' important.
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.
I sort of see it that way already. They couldn't do some of these things without magic. But the PHB doesn't specify how they do it; the descriptions don't say whether or not its magical. It's written in such a way that everybody can interpret them however they want. The word "spell" isn't used, but a lot of class abilities (c.f. Paladin, Ranger, Monk) are clearly magical without being described as such.
Which is why I think it's odd that the warlord
must be written to specifically say "this is not magic". Or, conversely, to provide a specifically non-magical mechanism, "your courage restores hope in your ally" or whatever. Why not describe it without locking it in to one or the other?