There's a general pattern of making social conflict systems use the same mechanics as combat systems - there's a few games that do this. Sometimes they go further than that and have no distinction between social conflict and combat and any other sort of challenge or conflict.

Dune 2d20 has a generic "conflict" system which revolves around moving assets between zones, and making "attacks" against the opposition, which reduce a hit-point-like total based on one of their attributes.

Diaspora is a Fate-based system, which similarly involves moving between zones, but is even more abstract. Zones might represent locations, but might represent topics of conversation - the goal might be to move to the innermost zone to learn an intimate secret.

Genesys has two HP tracks - Wounds and Strain. You do social conflict by making opposing rolls that damage the enemy's Strain until they are defeated. There's rules on complications that occur along the way, taking advantage of the narrative dice system.

Star Trek Adventures has a generic "extended task" system, heavily based on its combat system. A task essentially has "hit points" that you damage by making skill check "attacks". Arguing your case with a judge can be an extended task.

The One Ring has a "council" phase, which similarly involves a series of skill rolls based on the difficulty of the request, but this one is more tightly written to fit the theme of the game, rather than being a generic social conflict system.

Blades in the Dark and many other narrative games don't have explicit social mechanics, but don't have explicit combat mechanics either. Complex or difficult social situations can be modelled in the same way as any other complex or extended task, but using a clock that is "ticked" when you succeed at an action, similarly to "hit points" again.

Overall, there's quite a few variants, but there's a common theme of rebranding "attacks" and "hit points" to extend the task, even in narrative games like BitD. Note that, originally, hit points were added to D&D as a pacing and balancing mechanic, not out of realism or simulationism, so maybe it makes sense that trying to extend social encounters beyond a single roll might have the same solution.