I am not familiar with public debate. Before two persons start a public debate, is it a common assumption that you are going to hold your ground till the end, whatever the information provided by the opponent?
There is no flow of information and I could not see this form of acts as "communication" - it seems to be more like a kind of art/show/performance.
The goal of a public debate is to influence the perception of the many passive listeners, not the few other participants of the debate; There is extensive flow of information/communication, but it's simply not aimed towards the other participants of the debate.
So a key part of such debates becomes influencing or provoking others to talk about things that advance your cause and avoiding discussion of things that hurt it. E.g. if someone says "you eat babies" and you respond with extensive evidence that you don't, then that public debate becomes a debate about you being a baby-eater and not whatever you wanted to promote.
It's just not what public debate is. You see rookie politicians do it, but it's generally a mistake.
A huge part of what political debate is, is dominating the frame. The frame. The key facts, alternative or otherwise. The key question being debated.
Once those are established, the conclusion tends to be trivial.