I don't think arguing from shared premises has ever been as "ordinary" as calling one's opponent a witch, a hater of truth, and a corrupter of the youth.

That would probably be true in the case of trying to convince an audience. I think Luke referred to convincing your interlocutor.

Maybe in highly political arguments with an audience. I'm talking about even more ordinary kinds of convincing people than that.

For one thing, arguing from shared premises exposes the arguer to the possibility that those shared premises might, when justly examined, lead to the opponent's conclusion.

In which case you MUST concede the argument.