Social combat doesn't fit my playstyle (or my group's playstyle), simple as that. I wanted to codify some mechanics on how people could use their social skills for my home game at some point, and the players were largely opposed to the idea. To them (and after thinking a bit, I agree), we use abstract rules for combat because nobody at the table knows how combat would actually feel, let alone combat with magical abilities. The abstract rules of hit points and saving throws and Armor Class are all there so that we can create the fiction of what is happening in the combat despite having no actual combat experience. The abstract rules allow us to produce a result that's close to what we'd expect from fictional representations of fantasy combat (which were shaped by D&D in the first place, but that's an entirely different debate).
As for social encounters? Well, we all have experience with that. We know what it feels like when somebody can't respond to a knockdown argument (not that it happens a lot in real life), or when we correctly intuit somebody's disposition to us, or when we manage to lie through our teeth. If we try to use abstract rules here, it just stops feeling like... an actual social encounter. It feels more like a CRPG's attempt at replicating social encounters, which are needed in a computer environment, but make no sense when all sides in the encounter are actual human beings with some social experience.
So the only kind of social encounter rules I use nowadays are DM-facing rules to help me generate an NPC's initial disposition and some fast-and-loose rules on how to respond to general requests. The rules in the DMG (which set DCs for the DC a request would get depending on its difficulty), coupled with a 2d10 Reaction roll to establish an NPC's initial disposition (friendly-neutral-hostile) and some loose advantage/disadvantage rules when the players exploit an NPC's traits or flaws, are all I need. The rest would just get in the way of how everyone imagines a social encounter to be.