As others have noted - if you take out social skills, then the character's social skills are the player's. How necessary they are depends what you want from a game. Relying on the player's skill can work, so long as all the players are on board with it, and that's what they want.
I've played in games where the character's social skills are the player's. I've played in live-action games where the character's combat skills were largely the player's - if you personally couldn't swing a boffer weapon well, you died in combat. Heck, I played an engineer in a game where the skill was represented by my own ability to kit-bash mechanical things together. They were all good games.
For a general-purpose game, I'd tend to want at least some minimal social-skill mechanics in there.