This very much reminds me of British pantomime theatre, or at least a key trait featured in it. It incentivizes the audience to communicate with the actors, often by having them repeat (and slightly alter) statements.
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Audience participation is probably the most important part of British Pantomime tradition. Even the most serious and mature members of the audience, suddenly become uninhibited in their enthusiasm to join in. The audience is actively encouraged to cheer and clap for the Hero, and to boo the Villain whenever he or she enters. Heckling is also encouraged and can lead to some hilarious ad-libs from the cast. Here’s a typical example of involving the audience:
Ugly sister: “I’m much prettier than Cinderella”
Audience: “Oh no you’re not!”
Ugly sister: “Oh yes I am!”
Audience: “Oh no you’re not!”
If anything, this back and forth is formulaic, and your description of Carson's crowd interaction is too. The actor (or in Carson's case, host) makes a statement that's clearly intended to evoke a simple and straightforward response from the audience.