When we first meet Jonny Lee Miller’s John Major in the new season of The Crown, he’s in the back of a car listening to a radio bulletin. Home repossessions are up, and a recession is kicking lumps out of the economy. A bad vibe stinks up the back of his Prime Ministerial Jag.

Inside Prince Charles insists Major is “full of fascinating contradictions”: a working class boy from multicultural Brixton who ended up a Tory Prime Minister.

“Which makes you a far more interesting, more complex, more impressive person,” says Charles. You can almost see Peter Morgan poking his head out from behind a curtain, nodding furiously and mouthing wow what a very interesting and complex character.

preview for The Crown: Season 5 - Official Trailer (Netflix)

Major was, and remains, a plodding, managed-decline kind of Prime Minister. His story isn’t dull: as a teenager Major was a carer for his widowed mum, spent six months unemployed and missed out on a job as a bus conductor because he was too short. But Miller’s Major seems to constantly be shuffling around in a shaft of grey light, already half-dead.

In The Crown he’s there to be talked at by various royals, patting exposition back to them with a perfect forward defensive. The Queen slaps him down. Prince Charles butters him up. Prince Philip gives him a bollocking.

But the attempt to inject some zhuzh into a completely sauceless man suggests we’re at the end of something here.

After two decades where they were one of Britain’s biggest dramatic exports, we’re now scraping the barrel of interesting Prime Ministers to make state-of-the-nation TV and films about.

Liz Truss, Theresa May and David Cameron are all way too fresh for a convincingly dramatic arc, and Rishi Sunak offers little to work with except being a self-confessed Coke fiend. You could maybe try a Patrick Bateman thing with him, but again: too soon.

The big two of the 20th century are off the table too. After the Gary Oldman-Timothy Spall-Peaky Blinders vortex, Winston Churchill needs a rest. Meryl Streep and Gillian Anderson have given us more Margaret Thatcher than we’ll ever know what to do with.

We’ve only ever seen imperial phase ‘97 Tony Blair in TV drama, and the upwardly mobile New Labour years feel deeply alien now. Kenneth Branagh’s Boris Johnson was very good, but it’ll probably be another couple of decades before any portrayal of him feels like it’s not implicitly adding to his sense that he combines all the best bits of Cicero, Henry V and Rocky Balboa.

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And yet we keep trying to make the Great Prime Ministerial Drama happen. It’s an idea we’ve nicked from American prestige telly and film, where you’ve got The Good Guys (Lincoln, JFK, FDR, Washington and the rest of the Founding Fathers, sometimes Reagan) and The Bad Guys (Trump, Nixon, Bush Jr, sometimes Reagan).

We’ve gone hell for leather since Albert Finney’s magisterial Churchill in The Gathering Storm in 2002. And for Churchill, it’s probably fair enough. Thatcher too, in a more King Lear kind of way. (The third-most biopic’d PM is Benjamin Disraeli, who’s currently on a slightly improbable four.)

But a Prime Minister works less well as a cypher for a nation’s inner turmoil and self-regard than a president does.

It’s telling that it was a British politician, Enoch Powell, who observed that all political careers end in failure. There is always something pathetic about a Prime Minister’s last days, the usual desperate attempts to stay in post giving less Custer’s last stand than David Brent begging for his job back.

Presidents get send-offs and handovers and pomp. Prime Ministers watch as returning officers in school gyms announce that their justice secretary’s lost their seat as a grown man in an Elmo costume waves in the back of shot.

And you can’t get around it by just doing the bit where they were popular, because that’s not the fun bit. We don’t want President Bartlet, thank you, we want rats in a sack biting each other to pieces.

But with The Crown’s Major it might be time to call a moratorium. Even if our collective appetite for the big Prime Ministerial drama remains, let’s at least pivot to one of the leaders we’ve not given the time of day to.

How about Lloyd George leading the country through the First World War – and reputedly shagging about at the same time – before permanently tanking the Liberal party and then defending Hitler before World War Two?

Or cast Tom Hollander as a particularly feckless, shrugging, part-time paranormal investigator Arthur Balfour – a favourite phrase: “Nothing matters very much and few things matter at all” – and you’ve got yourself a six-part Sunday night romp.

George Canning and William Pitt the Younger both took part in duels while serving in government. And please, someone give Ryan Murphy a swing at The Assassination of Spencer Perceval: British Crime Story.

But please, I beg, whichever PM gets the biopic treatment next, we definitely need something less clonking than Major in The Crown. He goes down with the Conservative ship at the 1997 election, and has his last audience with the Queen.

“I do hope the history books will judge my premiership more kindly than the electorate,” he simpers. John, buddy: keep on hoping, because Daniel Day-Lewis isn’t about to start taking your calls.