Here is a scenario to illustrate the inherent flaws… Character X is not in combat and is attacked by an unknown aggressor, who succeeded in scoring a critical hit upon character X with a ranged attack from a long bow. Character X is critically wounded from the attack and has only 1% of his or her hit points remaining. The aggressor immediately flees after the attack. Combat therefore dose not continue, it’s over and character X is rather humped. The question is what kind of damage did character X sustain? Was it luck damage, morale damage, endurance damage, skill damage, or was it …wait for it… physical damage?

No, it couldn’t be physical, not from a fast moving projectile with a sharpened point.
Character X sustained hit point damage.
No, seriously. A hit point is what you make it out to be. Or rather, at the point that hit point damage is taken, the player can describe why the character is not dead yet. Maybe the character dodged out of the way, and is now tired. Maybe the character got lucky and the arrow just missed him, or conveniently hit something he was wearing or carrying. Normally, I would require that the arrow actually does "hit" in some way, so that the character sustains a non-lethal, non-hindering scratch or cut: a bit of physical damage, but not even 1 hp worth.
Think of hit points as a coupon for ice cream. When you actually cash it in, you get to choose which flavor you want.
When it comes to recovering from this wound, oops sorry I mean hit point loss, how is it done? Does someone come to yell at character X to walk it off, or sing a cheerful song, or does someone try to stop the bleeding and patch a nasty hole? This is not something you hand wave and move on. Seriously, if this doesn’t matter, then does the rest of the narrative matter?
Yelling is optional. A few quiet words of encouragement or a stirring speech will work as well. A cleric could pray, or a bard could lift the character's spirits with a song. Or a character could down a healing potion, use a healing poultice, apply medicinal herbs, activate a psionic power, or spend a few minutes to catch his breath and draw on his inner reserves of determination. Many causes, same effect: the character recovers hit points.
It's like getting another coupon for ice cream.
Now let’s say that character X died from that single attack. Now how does the damage get describe or attributed to? Did the arrow bad luck character X to death or scare ‘em to death?
No, the arrow hit the character in a vital spot and he died. Whatever he could have used to avoid the lethal hit just wasn't enough: he was too tired, he was out of luck, he wasn't skillful enough. Game over.
We're out of ice cream.
Another curiosity is that when other issues in gameplay involve morale, luck, skill, and such there is no hit point loss. Except maybe for endurance at times. This is a lazy half-assed approach and abstraction isn't solving anything but seeding chaos.
It has the advantage of simplicity and flexibility. Yes, the ability to describe
how your character escaped death whatever way you like, within plausible limits, is an advantage to some.
Why do you hate ice cream?