Bedrockgames
I post in the voice of Christopher Walken
Sure, I can see how you can build suspense and tension with dice in a social interaction. What I am saying is just a guess as to why there is a sense among some people that they are fine with combat needing mechanics but may not feel social interactions need mechanics. I think there is probably a lot of stuff that goes into the reasons. The expectation that combat have a kind of gambling excitement to me, struck me as a possibility. But that isn't to say others aren't going to want the same from social mechanics.I GM much more often than I play.
But the last two times I've played, the moments where I've held my breath as dice are rolled have been social, not combat. (In my Burning Wheel play I think there might be one combat every two or three sessions.) I (as my PC) tried to persuade my brother to throw off the yoke of his "master" (an as-yet unidentified NPC) and join me in restoring our family to its rightful place and status; I rolled the Command dice; and failed. My brother turned his face away, and rode off in his cart to complete the errand his master had sent him on.
For me, resolving that as a puzzle (eg what leverage can I use to turn my brother from loyalty to the master back to loyalty to family) would have been an uninspiring experience. Trying to persuade him, and then seeing the dice land as they did, was more like a slap in the face. It stung: just like in a real world interaction that goes badly, there was the sense of what might have been, but wasn't to be.
Thinking about this a little deeper I think where I come from with it, is combat is something I would rather not have mechanics for at all if there were a method that could capture the same organic free flowing approach to social interaction that would resonate with me in combat. Fundamentally the state of play you have in free form social interaction is my preferred state in an RPG overall (with moments of randomness of course to heighten the excitement and unpredictability. I use initiative for example. even though I can't stand its impact on the flow of things. It immediately changes the feel of play and creates a sense that we are in another game space for me. But I use it because when I have tried to do freeform, no initiative combat, when it works its great, but it only seemed to work for a small number of players (if I had a table of players who all got how to interject their actions without an initiative order, and we all gelled, it was brilliant, but 70 percent of the time that wasn't the case, and you'd usually have at least 1-2 players getting seriously tripped up by the lack of initiative order). Whereas I find I don't run into as many problems on the social interaction end of keeping things freeform and organic. And that is just initiative. And I find things are much more contested for me in combat. If someone says they stab my character with a knife, my mind isn't really sure if they would hit me or not. I feel I do need that random element (even if it were just something as gimmicky as the player needing to land a nerf ball in a nerf hoop at the table). Whereas in a social interaction I feel a lot more confident about how another character's words are going to land with my character.