In a recent column, Felipe Fernández-Armesto bewails the “intellectual and moral shortcomings” of the royal family and yearns for a Britain that admires intellectuals (“Duke of moral hazards”, 3 June). In so doing, he fails to recognise the appeal of the monarchy to ordinary people and elevates the notion of an elite caste of cognoscenti.

The popularity of the monarchy and royal family lies, above all, in their being a combination of the glamorous and the ordinary. Walter Bagehot realised this more than a century ago. The notion of the royal family as a “soap opera” is often used pejoratively, but expresses the truth of Bagehot’s insights.

“A family on the throne”, he wrote, “is an interesting idea. It brings down the pride of sovereignty to the level of petty life”. People can empathise with a family, with its generations, its individuals – for there are always heroes, heroines and black sheep – and with its weddings, funerals and crises, all of which they enjoy enormously.

Let us imagine the professor’s perfect royal family. One of the best-known portraits of the royal family is “Conversation Piece at the Royal Lodge, Windsor” (1950) by James Gunn. There they are, the “family firm” taking tea: George VI, his consort and his daughters, Princess Elizabeth and Princess Margaret. What are they talking about? Probably sport, Princess Margaret’s new dress, or the chances of a particular horse at Kempton Park.

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What would Professor Fernández-Armesto’s improved royal family be talking about? The exchange rate, recent developments in physics, and the interesting seminar Princess Margaret has just attended at the LSE? Which conversation would the majority of the British public find more interesting?

The English rather like academics, as they value knowledge and skills, but, sensibly, dislike intellectuals as “un-English”. They particularly dislike “public intellectuals”, an obnoxious breed found in France and the US, who feel they have a licence to bang on about anything and everything, and who have a tendency to find very clever reasons for believing very stupid things.

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The royal family has had only one member who fully qualified as an “intellectual”, Prince Albert, a man in tune with the intellectual life of his time – and the English disliked him heartily. George V hated highbrows, although he had misheard and thought they were called “eye-brows”, and he was a very popular king.

Prince Harry appeals to a broad section of society because he’s a soldier who likes a night out on the town; it’s a night out spent in expensive clubs, but not essentially different to a soldier’s night out in Newcastle or Cardiff. Would he be more popular if he had a doctorate in sociology?

Prince Charles, whom Fernández-Armesto does not mention, does bang on a bit on the issues of the day, but he has probably been more successful than accepted intellectuals in interesting the public in the environment and the questionable blessings of modern architecture.

What’s more, Fernández-Armesto rather overestimates the popularity of intellectuals in America outside of the East Coast intelligentsia. Ronald Reagan was, after all, the most popular president in the last half of the 20th century, but he was no intellectual, and George W. Bush’s folksiness did him no harm. What did for him was taking his country into an unnecessary war – but J.F. Kennedy, widely approved of by intellectuals and thought to be a bit of an intellectual himself, led the US into a more disastrous one. It’s probably about time we gave up pontificating on transgressions of sexual morality, but in this sphere the elected heads of state of the US in the shape of Kennedy or Bill Clinton seem at least as culpable as any “Randy Andy”.

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Jeremy Paxman, no faint heart when it comes to questioning hallowed national institutions, admits to embarking on his book, On Royalty (2006), with views not dissimilar to those of Fernández-Armesto, but he concluded that there was something to be said for allowing the state to be expressed through “fallible individuals”. As Lord Melbourne said about the Garter, the great thing about the monarchy is that “there’s no damn merit in it”.

Monarchy embodies the national ethos, which it expresses with ceremony, and embodies civil society as much as the state, but it is dangerously dependent on fortune, which determines the character of the head of state – though it is by no means evident that the hereditary principle produces better results in this respect than elections.

Above all, however, the very ordinariness and the imperfections of the family on the throne give the institution its cultural vitality. There may be no crown in the White House, but there’s no Tupperware either.