Two editions of D&D might hand wave hit points as being an abstraction, but all seven versions of the game only cause you to lose them when a physical event penetrates or bypasses your physical defenses. By the RAW, you don't lose hit points to blocked blows that were simply exhausting or a strain to defend against, and you don't lose hit points to any kind of miss.
Psychic/psionic attacks reduce HP without ever interacting with physical defenses.
4E, at least, includes attacks that deal damage on a miss.
Prior editions include effects that deal half-damage on a
successful save.
The purpose of D&D Next is to bring D&D back to baseline, not to turn the game into a dozen things it was never intended to be. And for what it's worth, for my part, the warlord falls outside of D&D baseline. The warlord is an attempt to hand wave several integral assumptions about the D&D universe, and it falls down on a number of counts.
The stated goal of D&D Next is
not 'to bring D&D back to baseline', but to provide a D&D that appeals to fans of all editions.
The warlord is essentially an in-game nod to the out-of-game absolutist opinion that hit points cannot be and are not meat. A warlord character would never describe what he does as healing, but in order for his class to be a viable player choice, it has to be able to provide damage amelioration on a level with the cleric, which means that at high level he has to be able to help allies recover from spell attacks like Disintegrate, which do not fart around about exactly what they are doing to characters. They are causing grievous bodily injury.
I am unable to consider any injury grievous when it:
1. Fails to impede me in performing any physical task: the game cares not whether I have 1 HP or 1 billion HP when it comes to running, climbing, swinging a sword, balancing on a tightrope.
2. Fails to impede me in performing any mental task: actual serious injuries are generally painful and distracting. They make it hard to concentrate on simple tasks, never mind complex ones. The game cares not whether I have 1 HP or 1 billion HP when it comes to performing mental tasks such as knowledge checks, answering riddles, or outsmarting a genius-level opponent.
3. Fails to have any impact on social interaction: People respond differently to those who are grievously injured than to people who are hale and hearty. The game rules are silent on this matter, and as covered in the previous two points, given that my character can have this 'grievous injury' and still act as an entirely healthy person, it's easy to see why. A person who's a stubbed toe away from death is apparently just as healthy in outward appearance as someone who can survive being stepped on by Godzilla.
4. Will recover on its own without any medical treatment whatsoever: Even in the slowest 'natural healing' options presented over the years, aside from those variations without ANY natural healing at all, even the most 'grievous' of injuries requires no medical attention whatsoever, as long as the character's HP are in the range of positive numbers. Any loss of HP is eventually erased merely by resting. A truly grievous injury would require immediate medical attention and specialized care, not just bed rest. If someone severs an artery, leaving them untreated and sending them to bed will quickly leave them dead: I guess 'grievous injuries' never include severed arteries.
I mean, why kowtow to a power when you can just learn to shout your allies' wounds away?
Why study arcane magic to learn how to throw fire at range when you can pick up a longbow and a flaming arrow?
Why devote yourself to a code of honour when anyone can smite the forces of evil just as dead without any such commitment?
Why master lock picking when the right spell (or a big enough axe) will open any door or chest?
Well, for one thing, there's more to the cleric than healing (and more to the wizard than range fire, and more to the paladin than killing evil, and more to the rogue than picking locks … ).
For another, even if the cleric and the warlord were exactly identical mechanically (which I've yet to see anyone ever ask for), the difference in flavour alone would lead people to pick one over the other. Some people
want to be the holy man, regardless of whether it gets them magical perks or not. Others want nothing to do with following a god, regardless of how many perks it might get them.
As near as I can tell, the only purpose the warlord really serves is to provide fuel to the fire of the argument over the nature of hit points. If you don't want magical healing in your campaign, then you don't want clerics OR warlords -- neither class obeys the laws of physics and nature as we understand them.
HP themselves never have and never will obey 'the laws of physics and nature as we understand them' (as nothing in nature or physics has hitpoints), so expecting things that interact with them to do so seems odd to me.
The purpose the warlord serves is pretty simple: making people who like playing the warlord (or playing alongside one) happy.
Not everyone who wants the warlord (and a warlord that has healing abilities, or even specifically 'spike healing') wants a ban on magical healing in their game. I have seen warlords played (and played them myself) in parties alongside clerics and other magical healers.