I'm a strong supporter of social stats and social combat
I think physical and mental skills (more physical than mental) get a regular pass because most physical is up to a roll of the dice and stats which can be optimized. Many players like to base the mental knowledge of their character based on their OOC knowledge or ability to Google, but neither really require much panache on the user-end.
In roleplaying or in MU (prose-based roleplaying), the expectation is that your words, actions, and intentions matter when getting your character's personality out there. It is a CORE element of the hobby that needs to be in place, but also, like GooglingKnowledgeSkills, replacing it with a quasi-meta agreement system and diceless pass/fail is a step in the wrong direction.
Really, the core of this topic is winners and losers, and when it comes to social combat, it doesn't matter how convincing the player feels their argument is. THEY are not the character. They are feeding lines to their character and rolling to determine, all dialogue validity aside, how convincingly deceptive, persuasive, or impressive their character translates those lines to their IC audience.
Many of these games are an ever-present source of stalemate due to entire crowds of players avoiding each other due to an inability to concede loss or victory because both sides want to win those situations, and doing away with social stats, dice, and social combat will solidify said 'You win when I say you do' approach as a standard.
It is my opinion that, instead, we work the other direction and start enabling people to have more IC social victories at the cost of leveraging IC risk, and one way we can achieve that is by letting dice aid in that process.
And, of course, never allow dice to justify things that are banned behaviors on the game.