James Gasik
We don't talk about Pun-Pun
Really what should be happening is, the DC of the social check should be based on the roleplay, but that's super subjective and nothing stops a DM who doesn't want something to occur from just saying "I don't care how well you argue, the King isn't giving you access to his treasury."*Because in Combat, you declare an action, the outcome is determined and than the action and outcome are described:
"I attack the Orc with my sword."
"Roll an attack."
"That's a 19."
"That's a hit, roll damage."
"10 Damage"
"Nice, tou all see, that Fin the Fighter draws his Sword, swinging at the Orc. The Orc tries to raise its shield, but it is to slow. Fin slashes wide open a big wound in the chest of the Orc, who growls in Pain."
In a social interaction, usually the action is described first, and based on that action and outcome is determined:
"Fin says to the orc: stand away or I will cut you!"
"Make an intimidation check"
"It is a 6"
"The Orc laughed and raises his Axe. Everybody, roll initiative."
So, in Combat, we have the Action declaration, the outcome determination and than the action and outcome description.
In social interactions we have usally the action declaration including the action description, then the outcome determination and then the outcome description.
For social interactions that can lead to a dissonance.
Like a players gives the best speech and roleplaying performance ever that in reality would make any king give up his kingdom, but than he rolls a Nat 1 and his character gets killed.
In Combat, the outcome is first described and then based on that, the action is described. If he rolled a 1 on the attack rolled, "Fin fumbled with the sword and couldn't bring it to bear against the orc" or a natural 20 "Fin, with on swing, hacks the Head off of the orc."
So, in 5e, if not be done carefully by the DM, how I describe my action in an social interaction doesn't have any bearing on the outcome. If I roll a nat 1, nothing what I said mattered. I failed.
Of course ... you could put the roll in front of the action description. Handle it like combat: declare an action, but don't describe it, with for the outcome determination and then describe the action based on the outcome.
"I want to intimidate the Orc"
"Make an intimidation check"
"20!"
Now he can describe a coom phrase. If he rolled a 1, he could describe how he stuttered and couldn't get the words out to really intimidate the orc.
But ... seperating the action declaration and the action description in social interactions kills any ryhthm. It slows it down to a crawl.
I'm not saying that this is a negative thing necessarily, some things should take more interaction than a single die roll, and some results could be abusive to game balance if they were "on the table", so to speak. But it does make social interaction murky; in combat, you are dealing with set DC's, like the AC of an opponent. And you know that if you roll a 20, you're going to be able to make a damage roll.
In social encounters, however, the DC isn't known, and the DM doesn't have to tell you that what you are attempting to do is flat out impossible until after you attempt it, which can sometimes feel like Lucy taking the football away from Charlie Brown.
As for the "state action first, then rp", while that would be ideal, that does interrupt roleplay, and as my earlier example pointed out, sometimes the DM can just waive rolls entirely if they like the roleplay enough.
This highlights the critical difference between most of the ways you interact with the game and social interaction. By and large, D&D functions by appealing to the rules of the game, making actions with relatively set parameters.
In social encounters, however, you aren't appealing to the rules directly, but appealing to the authority of the DM, their personal interpretation of the rules- which can come up in every aspect of the game, by design. It's why we have a DM.
But in my experience, social interactions are probably the most dependent on DM fiat (outside of edge case spell interactions, since many spells do what they say they do, even when that leads to confusing outcomes- a personal favorite is how you can't block a doorway with a Flaming Sphere, since you don't take damage from walking through it).