What I mean by this is, how do you describe to your players what weapon blows do against humans? It's pretty easy to say "your sword digs a foot-long gash into the dragon's hide. He seems more angry than injured," but what about the 18th level fighter they're facing down. Even a 3rd level fighter with a 14 Constitution will have on average 26 hp. That means the average person could stab him ten times with a dagger and he wouldn't be dead (2.5 average damage x 10 = 25 hp). It doesn't seem plausible to me (even in a world with magic and dragons, etc.) that even a really tough guy can take 10 stab wounds to the abdomen and still be fighting.
I've always thought of hits against a high-level humanoid to really be nicks and scrapes. The blows whittle away at his luck or divine favor or whatever you want to call it. High-level characters' bodies aren't really capable of absorbing those insane amounts of damage, they simply have some sort of inner reserve due to the fact that they are heroes.
You have almost all of the essentials of it. The argument you've just outlined is almost exactly the one Gygax outlined in the 1e AD&D regarding the correct way to view hit points.
Until a character is reduced to less than zero hit points, they are taking largely superficial damage. In a character without levels, hit points are basically meat of some sort, whether sheer bulk or super dense magical flesh.
But in a character with levels, the higher the level of the character, the less of a percentage of the character's hit points are meat and the more their hit points represent some heroic ability or skill to mitigate damage by evading it, turning blows that would be lethal into blows that are much less serious. So it's not the case that 4 or 10 hit points of damage ever represents a wound of a particular type. If a person is hit by a dagger and takes 4 hit points worth of damage, that might represent a relatively severe stab wound if the person only has 5 hit points, but for a person with 40 hit points they largely evaded the strike and took only a shallow nick or cut. Exactly how they did that is up to your narration, and if you are narrating wounds narrating how they evaded the wound is as important as narrating the location and scale of the wound.
When you suggest it is not plausible for a really tough guy to take 10 stab wounds to the abdomen and still be going, you are absolutely right and that is improper narration of the events. If the character had 38 hit points, and each blow did 4, the first 9 of those blows caused increasingly severe nicks and cuts, when the 10th was a deep wound to the abdomen that finally causes damage that can't be easily ignored by such a formidable hero.
Now, while those blows are in fact whittling away at the characters fortitude, luck, divine favor, spontaneous magical ability or whatever else is helping the character slide away from blows in the nick of time, they are in fact causing small amounts of damage to the meat. You can imagine if you will that a character with 38 hit points, struck with a blow for 4 damage, perhaps only takes the same damage that a 1st level character would associate with but 0.2 hit points of damage - perhaps not even enough to notice. But in the same way that a master pool player is more bothered by irregularities in the table, or an expert dribbler is more bothered by irregularities in a soccer field than an 8 year old booting the ball without touch, so too is the great hero's ability being slowly degraded by the damage that they are taking.
You might be asking, why bother with these nicks and cuts at all? Why can't we just narrate the 'hit' as not hitting, and instead simply abstractly remove the luck or stamina or whatever it is from the character. The answer really depends on the edition of the game, but certain problems in every edition of the game are avoided if you assume that every hit is a small amount of meat and a larger amount of non-meat. One problem with the "no meat" answer compared to the "percentage is meat" answer is that in most editions of the game, hits require a large amount of time to naturally heal from and recover from. In 1e, without the aid of magic, a high level character's body would not recover from such a beating for weeks, and even in 3e a not inconsiderable amount of time was required to heal from wounds. The "percentage is meat" answer there fore let's us deal with the problem of healing. But there is a further problem that if we go entirely to the "no meat" interpretation, that there is then a disconnect between the natural language of the game and what we are describing as the in game reality. If we say that there is "no meat" in damage, why do we call it damage? If we say there is "no meat" to a hit, why then do we call it a hit? And if there is "no meat" to damage, why do we refer to restoration as "healing"? I think it is clear from the language of the game that a hit is meant to be a hit, damage is meant to be some of wound, and healing is meant to refer to an in game reality of healing that is at least in some way related to the natural healing process everyone is familiar with from reality. Finally, there is an even bigger conceptual problem with suggesting hits do not hit and do not in some way connect with the target, and that is that it is a very common process in D&D that a hit triggers some special effect which really only can be explained by physical contact. That is to say, a hit that potentially poisons the target, cannot possibly have poisoned the target unless it in some way contacted the target, presumably at least contacting the flesh and often being associated with a nick or scratch. Thus, a wasp sting might not be deep on a hero with many hit points, but he's just as potentially effected by the poison as a lesser mortal with fewer hit points. And the same can be said of hits that do extra burning damage, or cause ability damage, or which paralyze, or which do life drain or which push or shove the target away. Pretty much all of these depend on some amount of physical contact, and its just most natural to narrate then all damaging wounds as having some physical trauma, however minor it may be, so that as Gygax pointed out, the high level character struck by many wounds is now covered with bruises, nicks, and cuts. They are not unwounded, but rather they have managed to avoid by heroic skill of some sort the serious harm that would have befallen a less skilled individual.
