Indeed. Not having played between AD&D (ending say 1992) and 5e (starting say 2015), it took me a while to realize (with help of some of y'all) that the whole "players self-assigning rolls" thing was an artifact of some of those editions in between. I have a player who is fairly new to 5e who initiates a non-combat skill roll at least once a session. I will just have to keep calmly reminding him to just give me a goal and approach and I'll let him know if a roll is even required. Hard to break the habits of prior editions, I suppose.
I guess that aspect of the game doesn't bother me, as long as the intent of the request is clear. Sometimes a quick "I make ___ roll" tells me everything I need to know; it's just a useful shortcut. Occasionally I'll ask for clarification. While I encourage people to state things in terms of what they're trying to accomplish, I'm just not that picky on how they communicate it. Same way that I encourage people to speak in-character but occasionally allow a simple "I tell them __". It's just not a big deal.
To me, the gist I got from the OP (the story seems to have shifted a bit, but it may just be clarification) comes down to how you handle social skills. So in this case we have the bard trying to convince the barbarian to do something. The furthest I would ever go is say something along the lines of "The bard seems to be sincere and makes a convincing argument" followed by "How do you respond?"
Where I think a line is crossed is telling the barbarian that he must do what the bard asked. Or the declaration that the player is not running the PC "correctly" because as a DM I thought they should listen to the bard. It reduces the barbarian to a set of numbers on a paper. We're in roll playing territory where dice dictate who the character is, not whether or not they can accomplish something they're trying to do.
Personally, that's the way I run NPCs as well. For standard guard #153, I may use the guidelines from the DMG for influencing disposition but for NPCs I've actually put some thought into I'm going to try to run them as unique individuals. To each their own.