I realise that these arguments are put forward, not from bad faith, but from prior commitments. Game mechanics intrude on roleplaying. They do so in many ways. Sometimes preventing the player from deciding to do a certain thing (a charmed player-character can't decide to attack). Sometimes deciding what they think (a player-character deceived by an NPC disguise will given facts in mind that are contrary to the truth).
With you so far.
On exceptions to general. The argument you put to my reading amounts to lack of narrow enough specification to satisfy you as constituting exceptions. You hold there is a general rule - roleplay - which is not a rule but a definition in context. Even taken as a rule, social interaction skills can be used - possibly should only be used - as game mechanics in perfectly well specified ways. There really is no lack of specificity in how to use them. And there need be no lack of specificity in the outcome of their use. When used in such ways, they will satisfy the conditions judged satisfactory for the use of other game mechanics. (And this is given that there was any issue with their specificity in the first place, which I do not concede.)
I think this is where communication is breaking down between us. The reason that I don’t see ability checks (social or otherwise) as overriding the general rule (or definition or whatever you want to call it) around players deciding what their characters do is not lack of specificity, but order of operations. Like, let’s say it was a rule that a successful Charisma (Intimidation) check could impose the Frightened condition on another creature. I still wouldn’t think it was appropriate to call for a Charisma (Intimidation) check to resolve an attempt to frighten a PC, because the basic procedure of play is for the player to describe their action, then the DM to assess its certainty and stakes, then to call for a roll of some sort to be made if needed to resolve that uncertainty, then to describe the results of the action. So, when a player describes that they try to frighten another player’s character by saying “boo” or whatever, (or, you know, the DM describes an NPC doing it, I guess), the DM then has to assess if this action can succeed or fail. Can saying boo succeed at frightening this character? Well, according to the rules for roleplaying, no, it can’t, because the player decides what their character thinks, feels, and does. So, it is not uncertain and therefore not appropriate to call for an ability check in the first place.
Some spells and other abilities, like Charm Person, contain specific exceptions to this general procedure. When a player describes their character casting Charm Person on another player’s character (or the DM describes an NPC doing so), the DM must again assess whether this action can succeed or fail and has meaningful stakes. Can the character succeed at casting Charm Person? Assuming they have a spellcasting feature and Charm Person is among their spells known and prepared, yes (otherwise, no, and the action fails without a roll). Can they fail to cast Charm Person? No, not according to the rules for spellcasting; there are no rules for a spell failure chance in 5e. So, the action succeeds without a roll, and we apply the specific effects of Charm Person. In those effects, we see that the target must make a Wisdom saving throw (which contradicts the general rules regarding the play procedure, but this is a more specific rule than that, so it’s fine), and if they fail that saving throw they are charmed and must treat the caster as a friendly acquaintance (which contradicts the general rules regarding roleplaying, but this is again a more specific rule, so it’s fine.)
On lack of uncertainty. This is a simple case of cart-before-the-horse. A DM not only may, but must, decide what is uncertain. They should also consider other factors, like stakes. It is up to the DM in every case to decide what is uncertain and where the stakes are high enough to matter.
Sure, but the criteria the DM uses for determining if an action is uncertain are the fictional positioning based on their own description of the environment, the player’s description of their action, and the rules of the game. The rules wouldn’t support the DM in ruling that a character who doesn’t have a fly speed attempting to fly is uncertain. They also don’t support the DM in ruling that a character’s attempt to force a PC to make a certain decision is uncertain.
There are no carve outs for social interactions in the printed rules.
I don’t claim that there are. Maybe my above breakdown of the basic play procedure will help demonstrate that to you.
You may believe that social interaction is never uncertain, but that is only because of your prior commitments on the matter. It is normal that DMs will differ on when they will and will not call for checks. The best claim to higher ground belongs to the many lines on the DM's remit, and not to a few words that are about how to roleplay.
I understand that you are unable to see it that way: perhaps that is as far as we can get.
I don’t believe that social interaction is never uncertain. I believe that, in the absence of a more specific rule contradicting the rules surrounding the procedure of play and roleplaying, an action (social or otherwise) that is made with the attempt to force a PC to make a certain decision is never uncertain.