From my perspective, slow healing is precisely what causes it to fall apart. Slow healing is only possible if every attack that deals damage results in physical injury.
I agree that slow healing only makes sense if every attack results in physical injury, but I disagree that it causes anything to fall apart. Rather, I posit that physical injury is the only way to make sense of it all, because any other model will create significantly more problems than it can solve.
It seems to me, that entails rationalizing how every attack, including an orcish greataxe or a giant swinging an oak tree, causes some small injury to the character, like a scratch or a bruise.
Considering the language of the game, that doesn't seem like much of a stretch. If an orc "hits" you with an axe, it causes "damage"; and since you aren't "dead" that means the damage was non-fatal. This is literally just taking everything at face value. Absolutely zero rationalization is required here.
Additionally, we somehow need to address why these superhuman individuals require weeks or even months to heal those bruises and scratches. In the real world, injuries typically heal in parallel rather than serially.
That seems kinda nit-picky to me, but it's the perfect place to add a house rule, if you feel it's necessary. If there's one place I agree with Gygax, it's that it would be inefficient to spend too much detail in modeling things that aren't important.
Obviously, attacks with an effect that require contact can be assumed to have made such contact. Hit points might represent some degree of physical resilience, but no more than we would expect of a tough soldier in our own world. Primarily though, they are more ephemeral factors (like the skill to dodge a deadly attack at the last second). Of course, in this context, slow healing makes no sense since hit points represent factors that you can recover readily, such as the fatigue caused by twisting out of the way of an otherwise lethal attack.
Of course, if hit points represent factors that are easily recovered, then slow healing makes no sense. But as you say, some attacks definitely
do make physical contact. If the giant scorpion's sting didn't actually pierce your flesh, then you wouldn't have to save against its effects, or take a lesser effect on a successful save. If you fall from a dragon, then you're going to hit the ground pretty hard, and knowing how to roll is not a sufficient explanation (and it's usually covered by a separate mechanic anyway, which just reduces the amount of damage).
So clearly,
some damage is physical. And the rules don't distinguish between physical damage and non-physical damage in any way whatsoever; if you try to explain
this 4 damage from a dagger as fatigue, but
that 4 damage from a dagger as physical, then it's weird for them to both recover at the same rate; doubly so, if that recovery comes from a warlord's inspiration. Logically, it makes more sense if all damage has basically the same nature, since the rules treat it all the same regardless. If damage could express itself in such a wide variety of ways, such that inspirational recovery makes sense for healing some damage but not other damage, then you'd expect the rules to make that distinction at any point. And since we know that at least
some damage is physical, the only logical interpretation is that
all damage is physical.
"Injuries" such as visible bruises and scratches aren't even necessarily hit point loss, since these might not impede the character's performance in a meaningful way. Under this definition, loss of HP does not necessarily equate to physical harm.
It's impressive that it hasn't come up yet, but yes, the alternative possibility is that
no HP damage is actually physical in nature. When you have something like warlord inspiration (or Healing Surges, or recovery Hit Dice) as a core aspect of the system, it does seem much more reasonable than the alternative, where all damage is physical. It does mean, however, that our model - which ostensibly exists to determine what happens when a bunch of people whack at each other with swords - doesn't have any way to express that anyone has actually been hit. Short of them bleeding out on the ground, which probably involved a physical hit, but which can nevertheless be recovered from using non-physical means.
And of course, you can still be stabbed by a giant scorpion, and the hole it leaves in you is left entirely to narrative rather than mechanics, since the rules don't concern themselves with the possibility of physical injury. In fact, you can be stabbed any number of times, and you'll be fine once the warlord inspires all of the poison out of your system.
I mean, I hope you can see why
that is not a terribly satisfying narrative. If the difference between a "hit" and a "miss" is the amount of effort they had to expend while dodging, then why are we even rolling when the outcome is that they dodge either way? Why are we bothering with such a complex system for measuring intangibles, but
completely ignoring substantial metrics such as bodily integrity? I mean, it may be a relatively more consistent approach than trying to walk the line with mostly-non-physical HP in earlier edition, but the end result doesn't really tell us what actually
happened; which is the whole point of using a statistical model in the first place.
