I want to use your Convince the Guard situation as an example...
I've noticed this come up more with the Perception-ish scenarios in modern D&D (including Investigation & Insight), than with Social scenarios... but I still see it come up on rare occasion with Social scenarios too... It's the player being at a loss for what to do. "I'm not sure." "I don't know what my character would do." Any variety of that. When that moment happens in modern D&D games, I've often seen players default to "Can I make a X roll to figure it out?"
...so getting back to your example, which I think you're using a modern D&D paradigm for, you describe 3 possible outcomes:
1) The player doesn't come up with a reason (or it's flat out bad) for the guard to let them pass. No roll. The guard doesn't let them pass.
2) The player comes up with a reason that the guard might let them pass. You set a DC and they roll against it, succeed or fail.
3) The player comes up with a compelling reason for the guard to let them pass. Automatically succeeds with no roll. The guard lets them pass.
The interaction revolves exclusively around the player's intent and the outcome is binary.
The OSR approach would look very similar for #1 and #3, but in the "might let them pass" it looks different. First, you might use a reaction roll to gauge the guard's attitude toward the party (which is moving beyond just the player's intent); for example a negative reaction might lead with a "Oh, I've heard of you. You're the ones that lit the docks on fire, aren't you?" Second, the "might let them pass" probably plays out as a give/take to the conversation in OSR; this breaks away from binary outcomes to mixed (negotiated) outcomes. For instance, the guard might want them to surrender any rods, staves, wands, or fire-starting materials to the city guard for safekeeping while the PCs are in the city.
I'm still formulating my ideas, but...
One of the problematic patterns I've seen in modern D&D's social interactions is two-fold: (1) player describes cool approach, GM asks for roll, it fails, player gets a let down moment, and as this happens throughout session player describes less and less in social scenes. (2) player describes cool approach as they reach for dice, GM says it's automatically successful, player gets a let down moment that they didn't get to roll and use the high numbers on their character sheet that they built their PC to be good at, so throughout the session the player describes less realizing that less description means more rolls.
Whereas one of the problematic patterns I've seen in OSR social interactions is that when there is uncertainty (i.e. "might let them pass"), players have less control over pacing of social interactions. There's no easy-out check. I've noticed this in "is this guy being duplicitous" situations the most because in OSR the player has no recourse even when it feels like their character should. The Persuasion check (or whatever), even if it's the GM calling for it, gives a bounding box of when the scene ends, more or less. What I've seen this lead to is certain players going radio silent in many social interactions, with one or two players dominating... sometimes this is fine for the group, but other times it's not... and yet it's the same sort of subtle effect as I described above – a sense of disconnect between the player's words/description/desires and the outcome.
I apologize for the length of my post as I'm still working these ideas out, but this is why I used the word bridging before. I'm noticing issues in both OSR and Modern D&D that seem (to me) to have similar underlying mechanisms.
