Agreed, I always felt like most of the fact checking that has become vogue in the past ten years is designed to comfort the people who already agree, not inform people who want genuine insight.
If you don’t have fact checkers, a debate loses all its value. Debates must be grounded in fact to have any value at all. Otherwise a “debate” is just a series of campaign stump speeches.
That could lead to a debate between the fact checkers, which would derail the debate.
Better to not have fact checkers as part of the debate, and leave the fact checking to the post-debate analysis.