Something ominous is ­happening in America. What looked like a trivial rivalry between two overpaid TV hosts, Jay Leno and Conan O'Brien, is shaping up as a the twilight of the gods. It all began last spring, when O'Brien succeeded Leno as permanent host of The ­Tonight Show, NBC's flagship late-night ­programme. Leno was given his own show in an earlier slot. Then David ­Letterman's winkie intervened: Letterman, star of the rival network CBS, confessed to a string of affairs with ­female colleagues, claiming he had been the victim of a $2m (£1.25m) plot to blackmail him. Overnight, his talkshow turned into a must-see soap opera.

With no one watching either Leno or O'Brien, NBC panicked, and made plans to restore Leno to 11.35 and shunt O'Brien to the other side of midnight. O'Brien started making sarcastic ­remarks on air, which culminated in him saying last Tuesday (in Spanish): "NBC is run by brainless sons of goats who eat money and crap trouble."

O'Brien is a vicious little Countdown winner of a man, all nervy smirk and Tintin quiff. Leno is a spoon-faced eunuch with a bizarre silver afro. So who cares whose show goes out when? Well, The Tonight Show has been ­going since 1954, and has had only four ­permanent hosts. It is the godfather of talkshows: a monolith, a whaleshark, a fixed point in the turning world of US television. If it had effectively ­become The Tomorrow Morning Show, that was a big deal. And those panicky ­reschedulings are seen as a symptom of something bigger: that the ­talkshow as a format, and the networks it ­sustains, are in crisis. As if to confirm this, O'Brien finally quit NBC at the end of last week, with a reportedly $45m (£28m) exit package.

Good, I say. If television has ­produced anything worse than the talkshow in its long history of lousy ­formats and hateful ideas, I'd like to know what it is. As a format, the talkshow actively works to purge everything it touches of sincerity or spontaneity, life or human joy. The tone of engagement is one of mirthless bonhomie, a ­pantomimed five-minute friendship designed to fool neither guest, nor host, nor audience into imagining that the host has the slightest interest in what the guest is saying, or the guest the faintest interest in the questions.

When a guest has a book to plug, the host – as if to make quite clear the transaction that's going on – reaches under his desk, pulls out a pristine hardback, and stands it upright on his desk so the camera can zoom in. A weathervane of the insincerity is that the corniness of jokes in the host's opening patter is positively celebrated. Letterman finishes his joke. It's awful. The band drops in a little musical sting: a rimshot, or a weary drum fill. Letterman's mouth twitches as if to pretend, after all these years, he's surprised by this, and he turns his last-season's-parsnip of a face in the direction of the bandleader to feign forbearance. Leno's shtick is much the same, though at this point he sometimes takes a pace back and half-raises a hand as if to say: "You guys!"

All this reflex jadedness is, I ­suppose, intended to be ironic or knowing. But it's ironic without ironising anything, and knowing without knowing anything. That constant blank smirk of directionless irony simply adds up to self-congratulation. Presenters such as Jon Stewart, of The Daily Show, have attempted to send up the talkshow format, to wrench it into something new. But the format proved too strong: instead of making the ­talkshow more Jon-Stewart-ish, ­Stewart ­became more talkshow-ish.

It's often pointed out, with either ruefulness or weird pride, that the US talkshow doesn't work in Britain. The last attempt to do a wholesale Letterman – with house band and all – was Channel 5's The Jack Docherty Show, and it died a death. I'm not sure even Jack Docherty remembers it very well.

But it's not as if we've been short of awful chatshows of our own. Think of Terry Wogan in the 1980s, bringing his beige guests on to his beige set, twitching his trousers up over his knees as he sat down and prepared to be avuncular. Or Gloria Hunniford, her face an oasis of orange in a desert of pastels. And Parky, a man who never asked a question that ended in a question mark when he could simply cue up a tinned anecdote with a statement: "You worked with Burton in the 60s. And you drank with him, too. Heh heh. Interesting times." Or think of Jonathan Ross, the current king of the format, with his guests looking politely pained as he asks them about what they get up to in bed.

Ross is a talented broadcaster, Wogan a brilliant raconteur, and I'm sure Parky is very nice in person. ­(Actually, I'm not sure Parky is very nice in person but let that slide; I bet Gloria is lovely.) Chatshows still blow – and if the media landscape in which the chatshow was king is vanishing, that's to the best. If this puts paid to a world in which hardcore punks Hüsker Dü can find themselves being ­interviewed by Joan Rivers, we can all die that little bit happier.