I think the fundamental problem is nobody does formal debates with rules and moderators (who actually do their job).
Its not like falacious arguments and bad faith rhetoric is a new phenomenon. They've been with us since the beginning of time. They are problems we have solutions to.
With fair rules and moderators. Political talk shows in German TV almost always have a moderator, yet they rarely intervene when people cut each other off or talk over each other - but they will immediately if a person takes too long to elaborate their point or touches subjects that are scheduled for a later part of the show.
That kind of moderation encourages bad-faith behavior instead of preventing it.
I think Jubilee and Munk Debates try to do this. The problem is that a super formal debate like what you're suggesting might be quite dry and boring for most people to watch so it wouldn't get a lot of viewership.
True, which is the fundamental problem - people like bad faith debate a lot more than good faith. The issue isn't that people engage in it, but that the crowds eat it up.
Its not like falacious arguments and bad faith rhetoric is a new phenomenon. They've been with us since the beginning of time. They are problems we have solutions to.