Meetings aren't easy. Sure it can help to grab a room, gather and talk and calm down but an existing dispute can also further escalate in a larger meeting—it's gambling. One does always loose after a dispute (in his point of view) and that's much harder to accept in front of many than in front of one. If two have already a dispute, sure then you should talk with them both at the same time and act as a moderator. But still it's a very complex dynamic process which is harder to control with more participants.
Moreover, you can often clear/avoid a dispute when you had lots of 1-to-1-meetings beforehand where you got a good understanding of peoples thoughts, fears, etc.