At some point the Sacred Norms Of Journalism dictated that it was unfair for journalists to use their brains when transcribing statements. Then after some complaints about this, Fact Checking was born, as somehow a separate - and novel! - function.
I don't think it's reasonable to expect moderators to do a running live fact check on everything politicians say, but nor is there much point to "moderators" who... don't moderate?
Replace them with timers, a buzzer, and a computer generated voice with scripted questions.
