Swarmkeeper
Hero
Pretty much. There can be other factors that affect the DC or grant advantage/disadvantage such as using leverage based on PC knowledge or previous interactions.
I have some great players who simply are not very eloquent, and sometimes have a hard time expressing their goal and how they're approaching it. I don't want to penalize them for it.
I feel like this is a bit of a common ground breakthrough here. Thanks.
I'm hoping you are now realizing that in our game, expressing a goal and approach is not truly difficult. "I want to convince the guard to let us past" (goal) "by dropping the name of the guy we met last session" (approach). No rousing speech, no special words, no extraordinary knowledge needed, no penalty for 3rd person roleplay. Perhaps using that in-game knowledge in the approach earns them advantage, just like in your game.
Not so different in the end, right? (setting aside your preference for being ok with "I roll Persuasion" and my preference for not being ok with it, of course)