Kobold Boots, interesting that you mention the bloodied mechanic, which opens up penalties (monsters get special attacks on you) and options. In a way that makes hit points a little more verisimilitudinous than they have been previously.
Think of HP as a combination of tenacity, endurance and paper cuts.
That works well for 4e, given how quickly wounds heal and that a sergeant shouting at you can cure them.
The problems with this approach (thinking of all editions here) are:
1) Why do paper cuts require so much healing magic to cure? For example in 3e a 100hp PC on 1hp would need more than 10 Cure Light Wounds spells to be fully restored.
2) Why (at least prior to 4e) do they take so long to heal?
3) The player becomes dissociated from the character, to use the Alexandrian's phrase. The player knows that his PC on 1hp is close to death, but the character doesn't. Metagaming is required.
Wounds healing in six hours and being cured by warlords are probably the two major issues people have with verisimilitude in 4e. They suggest hit points that are less physical than they have been in previous editions. Though, paradoxically, due to the bloodied mechanic, hit point loss that stays above zero now has more of an effect.
The Alexandrian's approach is that a wound is partly physical and partly non-physical. Say a 10hp blow means 1hp of real injury and 9hp of 'luck loss'. But how can the warlord cure that 1hp of real injury with his Inspiring Word? Could any real injury completely heal in a day? However I don't see a shift from 90% abstract hp to 100% to be that big of a change.
Upthread, Beginning of the End mentioned 3e's extraordinary abilities, which indicate that the secondary world of 3e D&D does not have the same laws of physics as our own, even when it comes to non-magical effects. Could that then be an explanation for the warlord and six hour healing? D&D land is just a strange place. If one accepts extraordinary abilities in 3e, I don't see why one couldn't accept this.
But I don't think that's the concept of D&D world that most people have. The implications of extraordinary abilities were, imo, never accepted. Most people who play D&D believe the secondary world is a place where everything works like our own until you bring magic into it. Natural healing and warlords just aren't magical.