Yes, the consensus model of dialogue is faulty, because it does not result in a coherent decision. With the consensus model, people do not often agree on anything that results in action. The United Nations is a good example of this. The groups talk for a long period of time, but do not actually get anything done or make any progress.
If we're trying to get to the bottom of whether an argument is true or better, it's important to have a debate format. Dialogue tends to just turn into people going into long-winded explanations of what they believe that continue even if their premise is false, whereas a good debate stops someone in their tracks the instant they start on a false premise and says "That premise is false so I have to stop you there".
American politics is just one example of the depth and scope of human interaction; metaphors to describe such a dynamic can range from the bar fight, where anything goes, to a great ocean with huge waves at the surface, and something entirely new and different bubbling up from the bottom...I have no answer for such a question!