This. The consequences of failure should be a change in environment narrated by DM. If the player wants to narrate the failure as well that's fine.
Furthermore, if the King asks the Fighter a question, and the player's response is to just answer the question, I hope that in most circumstances the DM doesn't call for a roll. It's kind of unfair to say, "The king asked you a question, and if you answer I'm going to force you to make a Cha check, and if you fail there will be consequences." That starts to feel like "skill check as required obstacle".
Now, if the party is there because they want something, and the king refuses to deal with anybody but the fighter, and the fighter say, "Whooo-boy. I guess I'll have to try. Ok, I'm going to try to persuade the king to let our friend the rogue out of the dungeon, by pointing out that the rogue has the best chance of finding the (something), and that we promise to keep our eye on him." THEN the DM might say, "Ok, that's going to require a Persuasion check, but if you fail the king will be furious and...etc.