I previously wrote that hit points don't actually represent anything.
That's true, but it ignores the role they play in the mechanics of the system.
See, it's absurd to think that as a fighter progress in martial arts that they improve only at attacking and not at defending.
The obvious solution is a straight-up Red Queen scenario where every level the Fighter gets +1 Attack and +1 Defense. For whatever reason, D&D didn't do that, and has forever confused people since.
What D&D does is increase your Hit Points as a proxy for your increasing defensive abilities.
To understand this, we have to recall that in Chainmail, one hit equals one kill. Heroes take four hits, and Super Heroes take 8. Notice that it's no harder to hit Heroes - simply harder to kill them (or so it seems).
But is a Hero really any harder to kill than a normal man? Of course not. Sever his spine and he'll die like the rest. What he has is exceptional defensive ability that allows him to turn aside three blows that would have killed a lesser man.
Remember that in 0e, every hit die is a d6, and every damage die is a d6. This means that one die of damage (on average) removes one Hit Die. So your Level 1 mook is dead in one hit, and your Level 4 Hero is dead in 4. Just like Chainmail (but a little more random).
So it's clear that increasing HP is a proxy for increasing Defense (or AC, as D&D calls it), and nothing else. Every Hit Die is really a mulligan representing your increased ability to defend yourself.
How to reconcile this with healing rates and whatnot? You can't. That's because this is a stupid way to do things that causes no end of confusion, and is a prime example of an overloaded mechanic (i.e. HP is both life force and defensive ability).