So in the case of a Bard persuading a King, the DM's job is to, as fairly as possible, assess the likelihood of success. And that involves knowing their NPCs, what their motivations and personality and foibles are like, to determine that possibility. In other words, the DM is roleplaying the NPC. It is roleplaying when they say, "No, sorry, there's no way you're going to persuade him of that." It is roleplaying when they say, "Yes! The King jumps to his feet and agrees!" And it is still roleplaying when they say, "Hmm...that's tricky. Let me see a Charisma roll; you can use either Deception or Persuasion, depending on how you want to play it. 18 or higher and he'll agree."
So in the case of a NPC King persuading a Bard, the Players's job is to, as fairly as possible, assess the likelihood of success. And that involves knowing their PCs, what their motivations and personality and foibles are like, to determine that possibility. In other words, the Player is
roleplaying the PC. It is roleplaying when they say, "No, sorry, there's no way you're going to persuade him of that." It is roleplaying when they say, "Yes! The Bard jumps to his feet and agrees!" And it is
still roleplaying when they say, "Hmm...that's tricky. Let me see a Charisma roll; you can use either Deception or Persuasion, depending on how you want to play it. 18 or higher and he'll agree."
Again, the Bard didn't do anything to the NPC. The Bard just did something, with the objective of getting the NPC to do something, and the DM determined how the NPC responded to that something. Roleplaying, not mechanics.
just like the PC
EDIT: and I want to point out that in stating goal and approach, the goal...such as 'convince the king to let me marry his heir'...can be mistaken as being the "it" in "do
it to the NPC". But the purpose of including the goal is just to avoid misunderstandings and ensure that the DM understands what it is you're trying to accomplish. There's no binding mechanical effect that springs into being with the declaration of the goal. This, by the way, is also
@HammerMan's mistake in his example of "I climb the tree to find the cow.")
except you get the "I want to marry the kings daughter." "OKay, he doesn't seem likely to agree what do you do?" "I persuade him by telling him how strong my blood line is what a great hero I am and tell him the tales of the last few games."
"Okay, so roll CHa+persasion at DC 18,"
Bard player rolls a 27 (18+9)
so the DM says "Okay, you have convinced him of what a hero you are and how your blood line would help his, but since he still doesn't want the princesses to marry you, he offers you his niece."