Western society seems to have gotten the idea that "debate" is either talking heads trying to shout over each other, presenting prepared arguments to random unprepared people and claiming victory when it takes time to respond, or simply presenting opinions back and forth without trying to justify them. This is tied to the (independent but both incorrect) notions that whoever has the last word in a debate is the winner, and whoever wins the debate is necessarily right.

I think it would be valuable to somehow expose ordinary people to structured competitive debate, if only because it makes many of these falsehoods evident. This kind of debate uses the rules to select the positions of the parties and when they get to speak. Obviously the last speaker doesn't necessarily win, and the winner doesn't necessarily even believe their own position (so the debate doesn't prove that position right). Yet still, it's much better at educating people on the issues than any "debate" that most people have ever watched.

Unfortunately, structured competitive debate these days has gone off the rails. At least, college debate in the US has become ridiculous.

Moot court and mock trial retain some semblance of argumentation. But you would have to reinvent the kind of formal debate you’re imagining.

It’s hilarious. Robots talking as quickly as possible to gain points.

Strathern’s generalization of Goodhart’s Law at work.

Once a measure becomes a target it ceases to function as a good measure.

You may be right; I've been out of that loop for a rather long time now.