She may be a descendant of King George III, the principal raison d'etre for America's creation, and he the living embodiment of its success as an independent nation, but they come together as two individuals who know more than anyone the burden of leadership and a life lived under the glare of global fame.
Queen Elizabeth II has relished her meetings with the 13 presidents she has encountered during her long reign, and her tea with the President and Jill Biden at Windsor Castle on Sunday was a special moment.
(Even the President's spectacular breach of royal protocol in disclosing details of his conversation with the monarch -- she apparently asked for his impressions of Russian President Vladimir Putin and China's Xi Jinping -- did not dim the allure.)
The gathering capped what the British government will surely view as a hugely successful visit to Britain by the Bidens for the G7 Summit, one which went more smoothly than they dared to hope at the outset.
The timing of the summit favored the British hosts; home advantage meant Downing Street could capitalize on the relief all the world leaders clearly felt at gathering in person for the first time after a trying year of Covid restrictions and video calls.
Perhaps as a result, the summit was broadly judged a success, with more progress than is often the case at such events, including landmark agreements on vaccine sharing, tackling climate change and a new project to challenge China's Belt and Road initiative.
It was telling that it ended on a high note at the Castle, because the visibility of the Royal Family at the events surrounding the G7 represents the deployment of one of the United Kingdom's most potent weapons of soft power.
The thought and care which went into making the Bidens' trip as pleasing as possible hints at a nervousness in the British government around the President's attitude to the UK as it struggles with post-Brexit teething pains.
When a simmering row between the EU and its former member erupted on the eve of the summit over the somewhat prosaic issue of chilled meats -- inspiring inevitable headlines of "sausage wars" -- the US made clear which side its bread was buttered on.
Sausage jokes aside, the contretemps relates to the question of British goods crossing unhampered into Northern Ireland, which remains part of the UK despite sharing a land border with the EU member state Ireland, with all the questions of sovereignty that raises.
As a child of Irish grandparents, Biden is perhaps more wary than previous Presidents of any spat which threatens to inflame tensions among the parties to the 1998 Good Friday Agreement.
Thus the day before Biden arrived in Cornwall, at the southernmost tip of the UK, for the summit, America's most senior diplomat in Britain, Yael Lempert, was let off the leash to issue an unprecedented diplomatic rebuke known as a "demarche," making clear the President's concern at the prospect of rows relating to Brexit reigniting the Troubles.
When Biden used his first address on British soil to quote the great Irish poet WB Yeats' famous lines on Irish independence, "Easter 1916," Downing Street must have despaired.
Prime Minister Boris Johnson was already on the back foot with the Biden administration over the sense he was too close to the latter's predecessor, who once described him as "Britain Trump."
But for all the blond hair and populism, Johnson is no Donald Trump -- for one, he is a staunch supporter of tackling climate change (an agenda he has taken up more whole-heartedly since getting together with his now-wife, keen environmentalist Carrie née Symonds).
But the concern over how best to optimize this trip to put the Johnson-Trump relationship in the past was well-placed. British voters were near-universal in their antipathy for Trump, and despite Johnson's (and before him, Theresa May's) attempts to woo Trump's favor, there was a collective sigh of relief inside as well as out of government at Biden's victory in November. His ascendancy promised the welcome return of something approaching diplomatic normality in Washington.
Hence the rolling out of the big Royal guns for the G7. As well as tea at the Castle, the Bidens along with the other world leaders dined with the Queen, Prince Charles, Prince William and other Royals at the Eden Project on Friday night, while Jill Biden co-wrote an article on early years and visited a school alongside the Duchess of Cambridge, aka Kate Middleton.
And it soon became clear that despite his concerns about Northern Ireland, Biden was ready to play good cop -- gifting Johnson, who is a keen cyclist, a custom-built bike painted red, white and blue.
The President appeared genial and mollifying, telling Foreign Secretary Dominic Raab that given his own experience of losing his first wife and child in a road accident, he empathized with the family of Harry Dunn, the British teenager killed after being struck by a car driven by Anne Sacoolas, wife of a US diplomat who fled to the States claiming diplomatic immunity. The two sides agreed to explore the prospect of a virtual trial which would allow her to remain in the US while providing the Dunn family a form of resolution.
Soon after becoming President, Biden declared: "America is back. Diplomacy is back." For all that Johnson has said he is not a fan of the term, it seems the "special relationship" between the UK and US is back as well.