It also isn't what anyone has argued for.
Well.... kinda! I mean, speaking for myself, I am kind of poking the issue with a stick, because as I said earlier, its easy enough to 'get it'. D&D started out based on a wargame and the essence of wargames is combat rules, usually with randomizers (dice) included. They also tend to at least pretend to some degree of modeling reality (WH40k and its ilk aside). It has been asserted that nobody really knows jack about combat in any realistic sense, and we all agree it cannot be 'played out' (even in LARPs really, but certainly not at the table). So the options are 'talk it through' or 'wargame it'. Talking it through kind of generally (maybe not for certain formulations of games) run us into the Czege Principle, unless it is left 100% to the GM to decide all consequences. Thus I take it that dice effectively are really a way for the GM to offload this burden. Since she cannot really say what would 'really happen' she's got to either rule according to some goals (agenda) or else submit it to the dice/mechanics almost entirely.
So, the question boils down to whether or not the situation is thus on the 'social conflict' side of the house. Personally I kinda think its pretty much the same. While people can certainly pretend that character action X produces reaction Y in some NPC, its pretty much entirely up to the GM. There could just as easily be reactions A, B, C, or D instead and they could trivially be justified by details of the character's backstory or nature that are simply too subtle to be included in any world description. People are extremely complex and while we can often judge an individual in real life with full access to various queues, even that is pretty dicey, let alone judging a mere 2 sentence outline of one which you cannot even visualize. The GM is thus in ESSENTIALLY the exact same situation as they would be in terms of combat, they simply have to either resort to a randomizer/mechanics, or answer "what happens when I do X?" according to some sort of agenda.
There REALLY ARE only a few elements available to any theory on why one is traditionally preferred over the other, at least by some people. They just prefer it! Combat has traditionally been using randomizers/mechanics and doing it the other way, while consistent, runs into matters of tradition. Meanwhile the argument against using mechanics in social conflict exactly mirrors that, tradition. Yes, you may feel more 'in character', but then we get to a final question about that. How do you achieve the notion that the GM is not simply following a script or their own agenda? If they are, and that is perfectly fine (which I guess it must be) then we finally land back at why that isn't acceptable for combat, and we are DOUBLE justified in concluding it can only be a matter of tradition and really nothing else. See what I mean?