Freshly installed as prime minister, Boris Johnson returned from Buckingham Palace to tell members of his inner circle that the Queen had said to him: “I don’t know why anyone would want the job.” His response to Her Majesty is not known. He might have replied that he had craved to be “world king” since childhood and securing the keys to Number 10 was the closest approximation available to realising that ambition.

In theory, prime minister of the UK is one of the most powerful positions in the democratic world. Like an American president, he or she is the public face of the country abroad and the central focus for the media at home. Unlike an American president, there is no term limit. So long as you can keep the voters and your party sufficiently content, you can have a very long reign. Margaret Thatcher and Tony Blair both did more than a decade. John Major is often thought of as a brief and miserable interlude between them, but even he clocked up seven years at Number 10.

The cabinet selections of an American president are subject to Senate approval. The British PM can sit anyone he or she likes at the top table. You can assemble a team of all the talents. Or, as Johnson has demonstrated, you can put together a cabinet of nodding dogs. Coalition government, with all the restraints and compromises that involves, is typical in much of Europe. The UK’s electoral system is designed to turn minority vote shares into single party rule. In very few other places will 44% of the vote deliver the stonking parliamentary majority secured by the Tories in 2019.

A modern prime minister may not be able to operate in the shamelessly corrupt manner of the first, Sir Robert Walpole, who used a secret service fund to buy parliamentary votes and general elections. But the 55th occupant of Number 10 would probably agree with Walpole’s cynical observation that all politicians “have their price”. The PM still has extensive patronage to wield and the guardrails against outrageous behaviour are extremely bendy. Johnson has parachuted his own brother, along with a band of Brexit and media cronies, into the House of Lords. Lucrative Covid-related contracts have been fast-tracked into the hands of Tory chums.

As Asquith once remarked, PMs are free to define the job as they choose. They can roam across all the activities of government, they can tap the country’s finest minds if they have the wit to do so, and they can seize the initiative on any cause that animates them.

Yet it is contended that the job has become dysfunctionally difficult in these thought-provoking books by academics specialising in study of the premiership. Prime ministers struggle to set their agendas and realise their goals. They come to office with their big dreams only to find that most of them crumble to dust. They try to make things happen by yanking at the levers of state, then complain that the controls are made of rubber. Prime ministers may look all-powerful as they strut about the national stage, but behind the curtain we often find a quaking creature constantly scrabbling to survive and frequently overwhelmed by the crushing pressures of the position. The frenetic pace of events and the rapid responses demanded by 24/7 media leaves modern leaders so busy firefighting that they have scant time to reflect or plan. Anthony Seldon wonders: “How much more effective and strategic might prime ministers be if they were allowed more space in their diaries?”

Mark Garnett focuses on an associated problem. From Thatcher onwards, prime ministers and their aides have been possessed by a strong impulse to centralise control of both power and ideas at Number 10. This has left the building and its primary occupant overstretched, while the capacity of Whitehall departments has been “hollowed out” and the status of ministers “diminished”. British prime ministers only loom so large over the landscape because the rest of the cabinet has become so small.

Both these books offer an intelligent and insightful account of the evolution of the role, but I am not persuaded that the job has become uniquely challenging or deserving of any special sympathy. Seldon dwells on the superior longevity of German chancellors, but what about the French? They have recently struggled to find a president that they like enough to re-elect. Both François Hollande and Nicolas Sarkozy were ejected from the Élysée palace after just one term. Emmanuel Macron, who faces an election next year, may suffer the same fate. If you think British politics is a treacherous game, how about the Australian snakepit? All four of Scott Morrison’s immediate predecessors as prime minister, two Liberal and two Labor, were putsched out by their own parties. The carnage in Canberra has been so gory that some emergency workers have reportedly stopped asking patients to name the prime minister, saying it was no longer a reliable indicator of mental health.

Joe Biden is endeavouring to make a brisk start as US president. His urgency is informed by the memory that Barack Obama achieved a lot in his first two years at the White House, but not so during the remaining six after mid-term elections had empowered the Republicans to gridlock him in Congress.

The notion that it has got harder to be the tenant of Number 10 is surely influenced by a recent run of occupants of the office who have been unsuited to it. Gordon Brown was a formidable chancellor, but a floundering prime minister. His most positive period was during the financial crisis when he could effectively go back to doing his old job. Theresa May’s introverted and unsupple personality quivered in the spotlight that falls on a PM. Six years in the challenging role of home secretary proved an inadequate training for Number 10. David Cameron’s essential glibness was found out when he recklessly promised and then lost the Brexit referendum that immolated his premiership. Seldon laments that Cameron had arrived at Number 10 with no previous ministerial experience and suggests that it is preferable for prime ministers to have been battle-tested in other cabinet posts. He reckons the job is best done by someone in their 50s, old enough to have gained some wisdom, but still young enough to have the stamina to cope with the relentless demands of the top job. Yet the cases of Brown and May suggest that previous cabinet experience is no guarantee at all of success in a role that is quite unlike any other in government.

Communication skills and the other qualities we associate with the idea of charisma are often seen as an essential prerequisite for a modern leader. But Johnson’s serial bungling of the coronavirus crisis has underlined the vast difference between being a potent campaigner and a diligent administrator and a clear-eyed strategist.

No, it is not an impossible job. Just a bloody difficult one that demands a wide spectrum of skills, the full set of which are possessed by very few people.

Lest we are tempted to get teary about the pressures on a modern prime minister, remember that the compensations are hefty. You get the use of a pad in central London and a lovely house in the country. The salary ain’t that bad and you are pretty much guaranteed a post-prime ministerial payday from corporate gigs and speaking engagements. Amazing as it may seem, there are people willing to drop more than £100,000 to listen to Mrs May on leadership and even greater sums for Mr Cameron’s tips on how to be a success.

• Andrew Rawnsley is chief political commentator of the Observer

• The Impossible Office? The History of the British Prime Minister by Anthony Seldon is published by Cambridge University Press (£19.99). To order a copy go to guardianbookshop.com. Delivery charges may apply

• The British Prime Minister in an Age of Upheaval by Mark Garnett is published by Polity (£18.99). To order a copy go to guardianbookshop.com. Delivery charges may apply