As has often been pointed out, they are in particular not actually debates. Not in any classic sense. But at least in one respect, that's not just a fussy technical matter.
Let me explain. I was a high school and college debater. In the few times I've been asked, I've said that the best preparation I had for journalism, after the basics of writing sentences etc., was high school debate.
In debate you had to construct an argument, and you had to anticipate that the other team was going to look for flaws. You could use rhetoric to your advantage in debate, and you could score points with criticisms of your opponents' positions. But in making your case--or disputing the other team's case--you needed facts. Convincingly organized facts helped a lot--but more than anything, facts themselves that had some basis in reality.
Because the most frequent and easiest question you were going to get from your opponents was always: what's your source for that assertion? What are the facts backing it up, and where do those facts come from? How were they arrived at?
It's true that what constitutes a credible source is as much in dispute between each side of whatever political polarity you chose, as the facts themselves. Nevertheless, it might add a lot of clarity to these so-called debates if once in awhile one of the candidates would ask those simple high school debate questions:
What's your source? What are the statistics that support your claim? Where do they come from? Who agrees with you? Which scientists, historians, psychologists, economists, epidemiologists, demographers, etc. etc.
You would think somebody would do that, especially when confronted with a candidate who very obviously is just making stuff up.
But they almost never do that. They just talk past each other. They disagree, without explaining the basis for disagreement. They shout.
These debates are basically sporting events with no actual system for keeping score, only the play-by-play and the stories afterwards. And judging the credibility of statements becomes the work of drudgy fact-checkers.
In high school, the fact checkers were the other team's debaters. That's a big reason they were there.
If their presence becomes a voice in your head, you become a better debater and a better journalist. In these "debates" there might be more basis for judging the winner and loser than a lot of disorganized impressions, if they actually debated on the basis of the credibility of their assertions.
That wouldn't be the only basis, just as it wasn't in high school debate. But it's an important one--especially since a President eventually has to deal with the real world, and its inconvenient truths.