I skimmed some of this thread, so apologies if I missed something. I promise that I'm not deliberately ignoring any point, and if one is relevant to something I'm saying, by all means point it out to me.
My main response to the OP is that the important difference, as I see it, is as follow:
"Damage" in some setting working differently than actual physical damage doesn't preclude roleplaying a character in that setting, because it doesn't preclude the existence of of people with motivations, emotions, beliefs, and so on. "Motivations", "emotions", "beliefs", etc. that work differently from the real thing are different, because substituting other things for those potentially rules out anything that can meaningfully be called "a character", depending on what is substituted.
And it's not even a simple binary, either, where sufficiently egregious departures from reality completely destroy players' ability to relate to their "characters", but anything less than that is fine. Rather, it's a continuum, where characters feel less like characters and more like weird abstract alien things the more weird, abstract, and alien their psychology is made.
I don't expect that every player even cares about that, but roleplaying a character is part of the appeal of a roleplaying game for a lot of people, and replacing characters with something else and roleplaying with some other activity is going to be unsatisfying on that front. In short, lack of psychological verisimilitude in particular is an issue in an RPG due to the target audience inherent in the very term "roleplaying game".
That all said, fictional characters in general often seem unrealistic to varying degrees, partly due to being written with goals other than realism in mind, and partly due to our understandings of others' and our own minds being rather less than perfect simulations. Some level of suspension of disbelief is necessary. And RPGs have plenty of goals other than character plausibility, with the relative importance of those goals varying from one gamer to another.
No one should be regarded as being entitled to make the game less fun for others. Some may be entitled to do things that make the game less fun for others, but never because it reduces someone else's fun. (I assume that that isn't actually what you meant, but, like, yikes! Phrasing!)
It's all well and good for your fantasy world to contain psychic kangaroos with laser eye beams, but calling them "dragons" is going to annoy people for being misleading if nothing else. And "dragon" is a broad term used for a wide variety of different creatures! "Human" is a word for a specific species in the real world, and most RPG players have a pretty detailed understanding of what humans are like, due to having encountered more than a few humans themselves.
For this and other reasons, the job of "humans" in fantasy, even more so than many other things called by familiar names, is to be indistinguishable from the real things they're named after under normal circumstances. So why would you call something "human" if it works differently than a human? Because it looks the same? But why does it look the same? Perhaps because you're trying to insinuate that it's something that it isn't?
I think that Quertus intended "HP" as shorthand for how Dungeons & Dragons handles damage to characters. But you're right that the basic model of having characters fall down when a number called "hit points" falls to zero can entail a lot more realism than that.
But, as you yourself have noted, it's possible to engage in real physical activities as well. Sure, that's the domain of LARP rather than tabletop games, but then why play tabletop games instead of LARP? Not just because they have a different name, presumably!
Citation needed.
Honestly, those all seem at least consistent with social interaction as a zero sum game, and thus less than ideal for, well, illustrating that social interaction doesn't have to be a zero sum game, and thus shouldn't exclusively be modeled as such.
The assumption that some form of communication will always be adversarial can certainly lead to weird holes in the rules. I've noticed that in D&D 3.5, for example, the Bluff and Sense Motive skills cover one character trying to trick another but not one character trying to convince another of the truth. It intuitively seems like being honest shouldn't make it harder to convince someone, and thus that one should still use Bluff which should probably be renamed to Persuade or such, and that a good Sense Motive roll on their part should help rather than hurt, but it's still a bit of work from there figuring out how to turn an opposed roll into a cooperative one.
That "honesty shouldn't make things harder" issue also rears its head in Exalted, where it seems to be a fundamental flaw of the system (in 2nd Edition, at least; not sure if 1st or 3rd are any different here). If the Manipulation character attribute covers any attempt to influence someone's behavior or attitudes, then it can be used for all social attacks (even if some of them can also be made with Charisma instead), because that's what social attacks are. And if it specifically covers the use of deception, that creates a bizarre incentive for characters with higher Manipulation than Charisma to work trickery into every social interaction, because that makes it more likely to work. Now, that may make sense for the Ebon Dragon (and his Exalts, who are themselves slightly Ebon Dragon), but the vast majority of characters are not the Ebon Dragon.
I quite like "Skill rolls are attack rolls, but the damage depends on the weapon" as an approach to "social combat". (Although to what extent social interaction should parallel combat at all is a different question!)
I'd expect for the positions of highest authority to be held by those most capable of the most mind control, and for them to limit the use of mind control by others, as with violence in real life.
The relevant idea is that naive predictions of human behavior can be wrong in systemic ways, not that any theory is "more true" than actual events, which is a preposterous strawman.
Of course, as you noted, this is a moot point unless a system actually tried to reflect some psychological theory.
Why not?
That's not a rhetorical question, by the way. Some people might answer with "Because the GM should never have a problem being obligated to have an NPC behave in some way", while others would reply "Because the GM should always be able to fiat any damn thing anyway". But yet others would say "It is neither necessary nor desirable to give the game master the role of either tyrant or doormat".