I think that @faraday's 4 (or so) points were a good rundown of why social systems are so hard to work into games, especially online games (@ZombieGenesis 's story shows that it's not just online games though). I think, however, that it all comes down to one singular point: Trust.
If you trust the other players not to screw with your character with the social combat system, not to push them into something that is totally against their morals, then you have fewer problems letting the dice make the (more minor) decisions for you in social situations.
If you trust the other player, then you're more willing to accept their view on potential modifiers for a social roll: "Oh, your character had a kitten that they loved growing up? Sure, I'll take a -3 on my attempt to get them to drown kittens." Sadly, there isn't a whole lot of trust out there in the MU*osphere (with good reason, read some of the Hog Pit threads if you doubt why), so when someone says, "My character had a kitten that they loved growing up, you could never get them to drown a kitten, EVER!" the initial response is often, "Oh, you're just trying to avoid the consequences of messing with my social-fu character" instead of "Interesting roadblock, could be fun to RP getting around (or not, based on how the RP and dice go)."
I've tried to design a system that allows for that sort of back and forth with modifiers and negotiation... but it still requires that you trust the other player at the end of the day.
As for social stats vs physical stats, even on PvE games, there's usually at least the possibility of another PC punching your PC (even if they aren't trying to kill yours), and usually you use combat stats for that. But if social stats can't be used against other PCs... well, they're less valuable. Granted, this is the same compromise we chose on the last couple of games I Staffed on (social stats only work on NPCs) because it's a nice clean line and still allows a social character to be created.