Curtseying is weird.

It’s so innately weird that there is probably no relaxed and normal way of doing it, although admittedly Theresa May manages to make unusually hard work of it. Greeting Prince William as they both marked the centenary of the battle of Amiens this week, she executed yet another of those grovellingly low dips that always make one think she is either about to fall over, or might have caught a heel in a grating. There have been unkind comparisons with Gollum from Lord of the Rings.

But the oddest thing isn’t that May perseveres with this most old-fashioned of traditions. It’s that the younger royals in particular – the famously modern and inclusive younger royals, who are forever suggesting that they’re just like the rest of us, really, underneath – don’t politely put a stop to a form of forelock-tugging that has so obviously had its day.

For there is something uncomfortable about the sight of a woman in her 60s ritually abasing herself before a man half her age, who has done nothing to warrant such reverence besides being born into his current family; who may or may not prove to be a good king in the distant future, but whose achievements are so far mainly limited to having been a helicopter pilot and then having some children.

Why on earth should elected power defer to inherited privilege in this way? Does William not find it as awkward and embarrassing as everyone else does? And if he does find it so, why doesn’t he let it be known that his future subjects should cut it out?

Curtseying or bowing is of course no longer compulsory, as the palace’s own protocol guide for ordinary mortals makes clear. It may be the traditional courtly greeting, but even the Queen will happily accept a handshake if that’s what people find comfortable. Jennie Bond, the former BBC royal correspondent, says she never bothered bending the knee because she simply couldn’t see why she should. Dickie Arbiter, the Queen’s former press secretary, classed curtseying in his memoirs alongside a host of royal customs “not necessarily right for modern times”.

May presumably still does it either because she feels the sort of reverence for the monarchy as an institution that is common among Tories of a certain generation, or because she remembers the almighty fuss about Cherie Blair refusing to do it, or because as a vicar’s daughter she holds a particular respect for the monarch’s position as head of the Church of England, or possibly a mixture of all three.

Another awkward curtsy. Photograph: Dominic Lipinski/PA

It’s a small thing, but it matters because in Britain curtseying (and its male equivalent of bowing) are the physical embodiment of a delicate constitutional question. They signify that prime minister and royal meet not as respectful equals but as inferior power greeting a superior one.

For the most part royal powers are, rather like a nuclear deterrent, all the more mighty for never being used. Theoretically, the Queen is entitled to form governments, and both government and armed forces serve her, rather than the other way round. What makes this situation at all tolerable in a mature democracy is that in practice, that’s not quite how it works. The Queen plays a chiefly consultative and ceremonial role, stays almost entirely out of party politics and is thus able to act as a national figurehead capable of bringing people together in a time of crisis. It’s a delicate balance, reliant on the wisdom and goodwill of those involved.

Right now, the rise of Donald Trump in the US and wannabe populist imitators here should be making us reflect urgently on how well this unwritten and mostly untested arrangement would cope with the election of someone genuinely dangerous. What rusty old brakes and backstops would we have if the threat were to come from inside our democracy, not outside it, and would it ever be acceptable to use them? But the longer-term question has always been what might happen if someone rather less benign than the Queen one day acceded to the throne. And every time May bends the knee, we are reminded of that possibility.

The line between respect and deference is a thin one, but you instinctively feel when it’s been crossed. I can still remember the shock, as a young lobby reporter, of watching my American counterparts applaud then president Bill Clinton after a speech – British reporters would have rather dropped dead than do the same for our prime minister.

A few years later, at a joint White House press conference given by George W Bush, there was a minor kerfuffle over the British press pack’s failure to stand up when both leaders entered the room. The White House reporters rose for their head of state; we Brits thought that was sappy, and bottoms remained firmly glued to seats, to the apparent irritation of the Bush team. But standing is what children do when their teachers enter the room, not how adults respond to people they’re supposedly holding to account. Again, it’s only a tiny thing, but culturally significant.

And like politicians, the younger royals can’t have it both ways. It’s all very well the Duchess of Cambridge wearing high street labels and being photographed pushing her own trolley around Waitrose, but her husband can’t expect us to take him seriously as a kind of everyman figure while simultaneously entertaining genuflections. If they want to carry on bowing and scraping within their own family – both Cambridges have been photographed greeting the Queen in this manner, and Meghan Markle curtseyed at her own wedding – then they’re very welcome, just as we’re all welcome to our own eccentric family traditions. But please, leave the rest of us out of it.

• Gaby Hinsliff is a Guardian columnist