Who can fail to have been impressed by the spectacle of President Obama's inauguration last week? I'll tell you who - the Queen. I bet she sat there watching it on an unpretentious four-by-three portable, while she sorted dog biscuits into separate Tupperwares, muttering: "It's bullshit, Philip! No carriages, no horses, no crown - it just looks like a bunch of businesspeople getting in and out of cars. It's as if the Rotary Club's taken over a whole country. And the new one's not even the son of one of the previous ones, unlike last time. I thought they were coming round to our way of thinking at last."

And she'd have a point. It might have been considerably grander than a new prime minister pulling up outside Number 10 and waving but, compared to the coronation, it looked like someone signing for their security pass and being shown where to hang their mug. And that's what comes of having an elected head of state. There's always got to be some fudge between the dignity and status of the office and the politician's desire to seem humbled by the occasion.

In fact, it's one of the most startling examples of politicians' self-belief that, as they assume offices of massive power for which they have striven, to the exclusion of all other activities, for decades, they'll still back their chances of coming across as humble. Now, there's an insight into the megalomaniac's mindset: "Not only can I get to be in charge of everything, I bet I can make people believe that I'm not really enjoying it so that, thanks to reverse psychology, they'll want me to stay in power longer!"

Whereas the Queen didn't have to pretend she wasn't enjoying the coronation; from the little bits of grainy footage I've seen, it's hilariously evident. A poor, terrified slip of a girl, the fluttering eye of a storm of pageantry, hesitantly mewing her lines, while thousands of incredibly important people in fancy dress behave as if she's the Almighty made flesh. That's what I call a show.

I don't envy the Americans their political system. I envy them their success, money, inner belief that everything isn't doomed to failure, attitude to breakfast, and teeth, but not their constitution. The fact that their figurehead and political leader is the same person gives them a terrible dilemma, especially when it was George W Bush. The man's clearly a prick (he says he'll wait for the judgment of history but, if the jury's out, it's only because they're deciding between personable incompetent and evil moron) but even his political enemies were squeamish about calling him one.

They had to respect the dignity of the office and couldn't come to terms with the American people having bestowed it on someone who can't string a sentence together and would only make the world worse if he could. To completely let rip in slagging off Bush would have caused collateral damage to national prestige, not only by undermining the office of president but, more important, by openly admitting how far America is from being the classless meritocracy it claims.

We in Britain have no illusions about being a classless meritocracy and it's therefore thoroughly appropriate that our head of state should be chosen by a method dominated by class and utterly and openly devoid of regard for merit. Separated from the nitty-gritty of politics and power, our monarchy can be a focus for both national pride and self-loathing, the latter being much more archetypally British than the former. A harmless little old lady dutifully going about various tasks she finds stressful seems about right for our national figurehead - neither better nor worse than we deserve.

Don't mistake me for a republican. I genuinely like this system. It means the most powerful man in the country still has to kowtow to someone (other than the president of the United States). It encourages tourism. The royal family, while nominally our betters, are in fact our captives and an interesting and profitable focus for media attention. It's as unfair as life; the royals can't escape and if you want to become royal, you basically can't. It's a more or less functional arrangement that no one would ever have had the wit to devise deliberately.

Which is why Liberal Democrat MP Evan Harris's attempt to fiddle with it is so enervating. He wants to change the Act of Settlement whereby Catholics can't marry the sovereign and end the discrimination against female heirs to the throne. He thinks this will make the monarchy more fair. I suppose it will, in the same way that throwing some bread into the Grand Canyon will make it more a sandwich.

The monarchy is overwhelmingly, gloriously, intentionally unfair - that's the point. The defining unfairness is that you have to be a member of that family to be king or queen; fringe unfairnesses like their not being able to marry Catholics or men having priority in the line of succession are irrelevant in that context. And what's so fair about primogeniture, which Harris is not planning to touch, or the sovereign having to be Anglican, which is also apparently fine? He wants to spend parliamentary time, mid-credit crunch, on a law aimed primarily at helping Princesses Anne and Michael of Kent.

When will people get the message? If you want a fair system, have a republic, elect a president and live with some arsehole like David Cameron giving a speech every Christmas Day afternoon, bitter in the knowledge that you asked for it. Otherwise, we should stick with what we've got, rather than trying to tinker. No abdicating, no skipping Charles, no changing weird ancient laws. We get who we get because we'd rather live with the inadequacies of a random ancient structure than the inadequacies of one designed by Brown and Cameron.

The monarchy's not perfect, but it's also not harmful, powerful or, and this is the clincher, our fault. The inevitable imperfections of anything we replaced it with would be.