If nothing else, the sheer classiness of the route for Margaret Thatcher's last journey was of a piece with the grandeur of the occasion. It passed through three of London's greatest buildings on its way to Mortlake, where she was cremated: from the more than millennium-old Westminster Hall to St Paul's for the funeral itself, and on to that other high watermark of Christopher Wren's career, the Royal Hospital in Chelsea, where her ashes were finally interred.
For this was a state funeral in all but name. The lavish military honours - the coffin, draped in the Union Jack and topped with white roses from her family, arrived on a Royal Horse Artillery gun carriage - were no less distinct than the pomp inside the cathedral itself.
The 86-year-old Queen, clad all in black, and the Duke of Edinburgh were met at the West Door exactly 15 minutes before the service by a reception party including the Archbishop of Canterbury and the Lord Mayor of London, robed in scarlet and carrying something called the Mourning Sword. All this executed with the precision for which British pageantry is justly famous.
The music, climaxing with the adaptation from Holst's Jupiter for the patriotic hymn I vow to thee my country, made glorious use of the acoustics of Wren's soaring dome. This meant, however, that those worried a ceremony of this magnificence was somehow inappropriate for a politician - who for all her qualities was not Churchill - would not have their fears allayed.
It may be unfair to suggest there was a hint of "L'etat c'est moi" (I am the state) about the service; but there were times - despite the genuine tears of Chancellor of the Exchequer George Osborne and others - when its solemn obsequies were reminiscent of a coronation.
Faced with a difficult task, the clergy did pretty well. David Ison, the Dean of St Paul's, welcomed the huge 2000-plus congregation by declaring they had come to "recall with great gratitude her leadership of this nation, her courage ... and her resolve to accomplish what she believed to be right for the common good".
Like the Dean, the Bishop of London, Richard Chartres, stressed her well attested "personal kindness" including to those who "were not, in the world's eyes important". And in a much needed flash of humour, he recalled her grasping him by the wrist at a dinner and telling him "Don't touch the duck pate, Bishop. It's very fattening".
The clear, American-accented bible reading by Lady Thatcher's granddaughter, Amanda, was a timely reminder that this was also a family bereavement. And as at many less grand funerals, there was the temporary soothing of old enmities, Boris Johnson sitting beside Michael Howard who sacked him from the Shadow Cabinet for fibbing about an extramarital affair, and Cherie Blair chatting to Gordon Brown.
Despite the 11 serving Prime Ministers paying their respects, the international presence was borderline B-list. But here, too, there were ironies of long-forgotten history. Was Dick Cheney, who read Mikhail Gorbachev so much less well than Prime Minister Thatcher, repenting his brutal dismissal of his capabilities when she was courting the Russian leader?
Was her contemporary, the Canadian ex-Premier Brian Mulroney, wishing he too had been forced out like her rather than end as the one democratic Prime Minister with lower approval ratings than the level of interest rates in his country? And what was going through the mind of the Queen, now that we know from the most faithful of all Thatcher lieutenants, Lord Powell, that the Palace did indeed fret the South African policy of the time might endanger the Commonwealth?
The danger of summoning the full "non-political" panoply of the state to bid farewell to a Prime Minister - albeit a hugely successful one who certainly changed Britain as only Clement Attlee did in her lifetime - is that it suggests a Conservative PM has a place in history "beyond politics". Which she hasn't.
But as Bishop Chartres eloquently reminded the mourners, she was not just a "symbolic" figure, but one subject to "the common destiny of all human beings". Here, he said, she is "one of us".