But they don't get run through with swords, disembowelled etc.
In the fiction, they suffer injuries and carry on due to their resolve.
In 4e D&D, PCs are set back by various sorts of attacks and opponents, and carry on due to their resolve and the support of their companions.
How is 4e failing in this respect? In what way is it incoherent or contradictory?
Whether X is complex depends on both X's inherent and relational properties.
The consequences of insisting that hp loss and restoration is a measure of nothing but physical injury is that the game ceases to make sense. That is a type of complexity, in the sense that the game now includes fictions that can't be reconciled.
In all versions of D&D, AC is both toughness of shell/skin/armour, and quickness at dodging, blocking and parrying. Hence why armour, shields and DEX all add to AC.
Does a ring of protection create a forcefield (and so contribute "shell" AC) or does it deflect blows (and so contribute "shield" and/or "DEX" AC)? The game doesn't tell us. And doesn't need to tell us. If desired or necessary, this can be narrated as the participants (typically, the GM) see fit.
This does not stop AC being a relatively simple combat adjudication system compared to many alternatives. Eg in RQ, the toughness of the armour/shell, the quickness of the dodging, the deftness with the shield, are all broken out separately establishing 1:1 correlations between these mechanical elements and the corresponding fiction. But RQ combat is more complex than AD&D combat.
In AD&D an attack misses. Did the target dodge? Did the attack glance of the target's armour? The game rules don't tell us; either someone (in my experience most often the GM) narrates something, or else nothing is narrated and we just know that for some or other reason the attack did not set back its target.
In AD&D and attack hits, for 7 hp of damage. Was the target cut? Bruised? Their head cut off? We don't know any of these things until we compare the hp of damage to the target's remaining hp. For instance, a character with 1 hp remaining who loses 7 hp dies, according to the AD&D rulebook - having been reduced below -3 hp by a single blow - and hence may well have been decapitated. Whereas a character with 100 hp remaining who loses 7 hp clearly has not been decapitated, and perhaps has not even had their skin pierced: they may just have been grazed or bruised, and the real set back is to their stamina and resolve.
4e D&D does not introduce any challenges of narration that are not already present in AD&D, and at least in my experience generally makes the narration clearer because the effects associated with the affliction of hp loss help make clear what, in the fiction, is happening.
This is a problem entirely of your own making. You are introducing notions like "hit points are physical injury" and that hit point loss is a type of linear continuum, none of which are asserted by the rulebook, none of which is implied by the rulebook, and none of which makes any sense.
Say a character is hit be a fireball and loses 20 hp from fire damage. This tells us that the heat and flame have set them back to some or other degree; what degree will depend on their overall hp total, or even more precisely on their healing surge value, which is by default a quarter of their hp total but can be increased by various character features. When they recover hp due to having their resolve firmed up, they are no longer set back. Much like @Imaro's action hero, they have regained their will to strive and fight on. They are no longer tired and worn down and hence vulnerable to a lucky or skilled or sneaky blow.
There is no contradiction or "cognitive gap" here.
I reiterate that this is a problem of your own making, brought on by insisting that there are two categories of hp loss and hp gain, although nothing in the 4e D&D rulebooks supports such a claim.
Again, here you assert that these two things are completely different, but in the fiction of 4e they are not. As I already posted upthread, 4e D&D posits that heroic resolve, and the support of one's fellows, enables a person to go on despite injury, to overcome the setbacks that being attacked by sword and arrow and dragon's breath cause. In this respect it somewhat resembles @Imaro's action hero, although with more of an emphasis on the support/fellowship aspect (because for most 4e characters, more healing surge expenditure will be triggered by an ally's use of a Healing power than by drawing on their own reserves, especially in the thick of combat).
First, AD&D actually does have this problem. The only injuries that can be restored by a few days of bed rest are "resilience" ones - limbs do not regrow, bone and joint damage does not repair itself in this sort of time frame (if at all). So any narration in AD&D of hp loss as being more severe than bruising and grazing will produce incoherence as soon as characters recover by resting.
Second, you are very focused on the Wounds part of the spell Cure Light Wounds but not the Light part - whereas I have repeatedly pointed out that the spell is able to heal very serious, even mortal, wounds to most of the characters in the gameworld (people with more than 8 hp being nearly all above 1st level and hence rather rare specimens). No reason has been given why one but not the other word is so important - whereas the much more plausible understanding, in my view, is simply that Arneson and/or Gygax came up with a set of "scaled" adjectives for their level-scaled healing spells (Light, Serious and Critical Wounds); but did not have any strong conviction about what the use of healing magic on (say) a 4th level PC who has lost 5 hp actually looks like in the fiction.
