Though your main topic is the power imbalance, this nice post of yours also brings out the thinking-time imbalance: the difference between the outcome of a live debate and what the outcome would have been if one side or both had had a little more time to think. There must be a long, tragic history of debates that would have cast much more of the light of truth if the participants had been under less pressure or perceived less pressure. But people have enough attention span to watch debates, not more attention span than that. They don't have enough attention span to read philosophy papers. In democracies, public policies end up being only as good as attention spans are long.