What got me started on this was this Slate article about political types who won't appear together on TV:
The biggest offenders are usually the ones whose egos are too big to accommodate any company: Henry Kissinger, Zbigniew Brzezinski, Alexander Haig, and others who figure they have better uses for their time than debating some flack on the air. "They would only go on if they could do the show alone," says a former producer for Crossfire. "Brzezinski won't debase his cable currency by being a two-box," explained a current booker, referring to the practice of displaying guests on a split screen. Another booker cited Brzezinski's refusal to go on with Pat Buchanan—"probably because he thinks he's an anti-Semite." (An assistant to Brzezinski says: "It isn't true that he will only appear alone. He has appeared many, many times with other guests." Maybe so. But bookers say he doesn't do so willingly.)
Senators also tend to be finicky when it comes to sharing air time. Such was the case during the Democratic National Convention, when Sen. Chuck Schumer threw a fit upon learning that he would have to appear on The O'Reilly Factor with Clinton lawyer Lanny Davis. (Schumer had been told he'd be appearing alone.) When Davis refused to back down—"Unless Roger Ailes calls me personally, I'm doing the show"—they appeared together.
The food chain continues. Senators don't go on with members of the House, who in turn won't appear with anyone other than elected officials of their rank or higher. So why did Howard Dean refuse to debate his Republican counterpart, RNC Chairman Ken Mehlman, on the Today show in 2006? Host Meredith Vieira called Dean out on the air. Part of the reason was simply airtime, a Democratic spokeswoman explained; you can't say as much when you're on with someone else. But it's also a stature issue. Both were chairman of their respective parties, but Dean was a former governor while Mehlman was simply a former campaign manager (albeit a victorious one—something Dean didn't have on his résumé). "You don't want to put your boss on with Joe Schmo," the spokeswoman said while stressing that she was not comparing Mehlman to Mr. Schmo.
Yeah, it does bother me a bit when political types refuse to appear on the air together but pardon me for getting more worked up about showbiz figures who insist that they must be interviewed solo. It drains any energy that might have been present if they had to interact with other people. Unfortunately, celebrity egos nowadays are such that they wouldn't tolerate the situation that you saw in the Johnny Carson show video. Oh, and watch for Dean Martin furtively tapping cigarette ash into the drink of a completely unaware George Gobel.