Observation 1: Hit points are an abstraction which represent morale, fatigue, fitness, and so forth as much as health. (The classic statement of this being the fight between Robin Hood and Sir Guy of Gisbourne - erroneously identified in places as the Sheriff of Nottingham - from the classic Errol Flynn film; see this ENWorld post. The fight goes on for some time and the two figures don't wound each other until the killing blow, but Gygax seems to have imagined them losing hit points during the course of the combat nonetheless.) A lot has been written on this point, not least by me. But I don't think I'm saying anything controversial, either, if I suggest that the great majority of DMs tend to describe combat in a manner which suggests hit points are more concrete representations of health. What DMs tend to do (and I include myself in this), is that they describe the attack roll as being like the swing of a sword, and if it's a miss it's described as "you slash at the orc but don't connect" (or whatever), if it's a hit that does 1 hp of damage it's described as "you slash the orc across the shoulder" (or whatever), and if it's a killing hit it's described as "you stab the orc through the heart" (or whatever). This doesn't really square with this notion that hit points are an abstraction.
Observation 2: Hit points are actually fairly good at modelling what happens in a fight, in that wounds and injuries recieved, especially to the torso, tend not to affect combatants all that much until a genuine killing or knockout blow is recieved. A couple of times in my sporting life I've bruised or fractured ribs, or had a nosebleed or broken toe, and been able to finish whatever I was doing without much inconvenience. You don't notice the pain, often, until later in the day or the next morning when you can't get out of bed. This is due to the wondrous effects of adrenaline, obviously, and it's actually reflected quite well in D&D hit points, whose loss does not at all affect a combatant's ability to fight, but which do require healing afterwards. See also this short section from Barbara Tuchman's A Distant Mirror:
In one combat Don Pero Nino was struck by an arrow that "knit together his gorget and his neck," but he fought on against the enemy... "Several lance stumps were still in his shield and it was that which hindered him most." A bolt from a crossbow "pierced his nostrils most painfully whereat he was dazed, but his daze lasted but a little time." He pressed forward, recieving many sword blows on head and shoulders which "sometimes hit the bolt embedded in his nose making him suffer great pain." When weariness on both sides brought the battle to an end, Pero Nino's shield was "tattered and all in pieces; his sword blade was toothed like a saw and dyed with blood...his armour was broken in several places by lance-heads of which some had entered the flesh and drawn blood, although the coat was of great strength."
I've been considering these observations lately; and in particular I'm considering whether anybody actually needs the weird genuflection of hit points representing intangibles like morale and fatigue. I used to find Gygax's reasoning fairly convincing, to a point, but now I'm not sure. Combatants get injured during a fight by hits from enemy attacks. They don't really notice it during the fight unless it's very serious - because of the adrenaline and their own toughness. There's no great inconsistency there between the model and reality. The only tweak I might add to my games in future is something like this:
If a combatant loses 50% of his or her hit points in a given combat, from the next day onwards he or she takes a -1 penalty to all dice rolls until healed.
If a combatant loses 75% of his or her hit points in a given combat, from the next day onwards he or she is at half movement rate in addition to the above penalty, until healed.