Via Sunday-guest obsessive Steve Benen, I see that Jay Rosen thinks that the Sunday shows are "broken," and suggests that a little after-the-broadcast fact checking might help.
I have nothing against fact checking, but it has nothing to do with the success or failure of the Sunday shows. The main thing to know about the Sunday shows is that no one out in the country watches them. That's why they're on Sunday mornings! Normal Americans are busy sleeping in, or eating brunch, or going to church, or starting on weekend errands -- they aren't watching interviews with leading politicians and pundits.
The Sunday shows have one positive function, which is to facilitate communication between elites. Specifically, the Sunday shows have traditionally been a good place to float a trial balloon. The mechanics of trial balloons are inherently a little tricky (how do we know that it's a real trial balloon?), so it helps to have an established protocol. For fifty years or so, that's what the Sunday shows are for. As far as I can tell, they're still available for that purpose.
The rest is mostly self-aggrandizement (mostly the journalists, often the guests), and filler. I do know that parties have at least sometimes used the shows as trial runs for new talent (to see if they can competently deliver the party's talking points to top network types at a safe time when no one is watching). It's a nice thing that, in a democracy, the rest of the nation can tune in if we're interested, but no one is trying to convert the public on those shows, because the public isn't watching.
No one should care about the guests on the Sunday shows. No one should care about how the shows are run. No one should care about the Sunday shows, period. They just aren't very important.