Again though, let's not get too far into the weeds. We're not talking about "ways". We're talking about a single way. Same as a social check with an NPC. You don't allow a persuasion check to force an NPC to do something that the NPC would never do. So, why would it be any different for a PC? The effect has to be plausible, same as it is for an NPC.
The effect has to be plausible but the mechanics don't need to be the same. As I said to Lanefan, this is to help provide balance, to help prevent the GM from making their NPCs untouchable.
So the example of giving away a magic item is right off the table. No NPC would ever give away a magic item based on a persuasion check (barring specific examples of course). So, why would a PC? Now, running away because your courage failed you in the face of seeing horrific things done to the person beside you? Perfectly plausible. The fact that the PC's NEVER suffer any sort of trauma or anything like that is far less plausible at the end of the day. Your character can never be influenced by a persuasive argument? Not very plausible. So on and so forth.
The character can be influenced lots. The player is the one who allows the influence. Good players will allow themselves be influenced appropriately. The reason I said that you can't enforce it is that for a game like D&D, which doesn't emphasize working together to tell a story, you will get people who don't care and who try to game the system. In a narrative game, you won't have this sort of problem--at least not nearly as much, because the game is
built around the narrative.
And who says that the PCs can't suffer trauma? In Daggerheart, as an example, with one of the death moves you get a Scar. While you
have to cross out a Hope slot, you
choose the narrative effect of the Scar. Suggestions include "a physical scar, a painful memory, or a deep fear." D&D can easily do something like this. Not with the Hope slot, of course--although I wouldn't mind
too terribly much if they brought back the permanent reduction to Constitution upon resurrection, like in AD&D--but with the narrative effects.
(Mind, from what I've seen, most D&D players aren't even that cool with taking a level of exhaustion after being dropped to 0 hp, so the -1 to Con almost certainly wouldn't fly.)
There's nothing saying you can't have a similar house rule--or even an official rule in a future update/edition to the game--that's similar. "When you die, you suffer some sort of trauma of your choice, here's some examples."
But note that trauma is
not the same thing as in "run away because you rolled badly on a morale check against a bunch of orcs."
Comparing a single event in the course of a campaign to the death of the character seems a bit over the top no?
No. This is a morale check we're talking about. It will likely happen, at minimum, once every combat that's of Hard or greater difficulty, which likely means once few game days. So, potentially hundreds of times over the course of a campaign, as opposed to once to a handful of times a character dies.
It's like
@Maxperson's examples of how losing control of an NPC for a single check is okay because he has millions of NPC's, but is totally different from a player losing a tiny bit of control for a short period of time in a campaign.
Heck, you even double down on the players not being trustworthy with:
So, players cannot be trusted to act in good faith, thus we should not have social rules.
We're not talking about a social rule or even a game or genre expectation. We're talking about a game mechanic. Those are very,
very different things. And D&D is not a narrative-focused game. It's a game that focuses on the mechanics.
And again: there are no other mind-compelling effects in 5e that aren't magical or originating from a super-deadly monster of some sort like a dragon. So why should a nonmagical effect with a mundane origin be treated like one of those?
(And as I pointed out, despite what you said, Vex (the weapon mastery effect) merely says what the effects are; they don't tell you how the opponent will react. Because it's a nonmagical effect with a mundane origin.)