Ironically if you watch UK Prime Minister's Questions it consists primarily of point-scoring and jeering, with occasional excursions into triviality.

On occasion in Parliament you will find people delivering impassioned, carefully researched speeches .. to an empty room.

The prerequisite for discussion has to be willingness to listen and finding a commonality of view, both of which are in very short supply these days.

Much of that is due to incentives and not an inescapable aspect of public fora. Two notable examples that stand out in my mind of "people I probably disagree with about some things but trust highly" are HN's very own gwern, for exhaustive research, and Scott Alexander of Slate Star Codex. Somehow they have hacked, avoided, or self-disciplined their way into good-faith engagement without giving up ground to do so.

Integrated fact-checking would go a long way in political debates; gwern provides his own and S. Alexander, while less exhaustive, is relentless in analyzing his own biases and hewing to rhetorical charity. They would be less remarkable in a world where political debates had integrated fact-checking, as politicians would have to adapt.

Speeches to an empty room are still being read into the record (Hansard).

This is exactly right, and isn't a new problem either - it's literally always been the case.

I would almost argue that public debate doesn't really matter - it's always just a small handful of activists who get things changed (for better or worse).