When you boil it down, this is largely because it has never been more important to the people who elect them: in today's scary, complicated, interconnected world, there is something reassuring, almost atavistic, about seeing an athlete symbolising all that is best about your country take on the rest of the world and beat them fair and square.
Much good, for sport, has come of this state of affairs - notably the unprecedented wads of money, public and private, being lobbed in its direction.
But the rather overblown significance that tends nowadays to be attached to elite sport seems also to be encouraging more questionable phenomena.
One of these is what I am going to refer to as diplo, or diplomatic, doping.
I don't know if anyone keeps statistics on this sort of thing, but it seems to me that the number of athletes either switching allegiance, or deciding to represent a country that, by any objective assessment, is not the most obvious choice, has been on the rise in recent times.
In one sense, this is just a reflection of modern life: in a world where international travel and communication is a gazillion times cheaper and easier than ever before, it should come as no surprise that so many of us forge trans-national attachments.
It sometimes seems, indeed, that nearly everyone in the current generation of elite athletes can claim legitimate allegiance to more than one country.
Poor Adnan Januzaj, the Manchester United football prodigy, may soon have to make up his mind between as many as six countries that he might eventually qualify to play for.
But I wonder if the extent of allegiance switching in recent years doesn't also reflect a rising intensity in the battle among nations for sporting success and the spin-off benefits increasingly associated with it.
And, if it does, I wonder if additional steps ought to be taken to counter it.
To answer these questions, we should first think about what, if anything, is wrong with allowing athletes to switch nationality at will.
Would we lose anything of value by permitting, say, a badminton player to move from Iceland to Equatorial Guinea as easily as a professional footballer might be transferred from Juventus to Chelsea?
Should it be OK for a Chinese table tennis player to sign a four-year contract to represent, I don't know, Paraguay?
What if we went the whole hog and implemented a football-style transfer market, ensuring that the country which developed the athlete would, at least, receive something for its trouble?
Governments, after all, have grown accustomed to investing significant sums to develop Olympic talent; is buying the end product of someone else's development programme not simply a different, and potentially more efficient, way of achieving the same end?
I should say that I have a certain amount of sympathy for Chinese table tennis players, or Brazilian footballers, who would be good enough to play for many other countries but who, because of the depth of their native country's talent pool, have little hope of experiencing international competition.
Nonetheless, it seems self-evident to me that this is not the way to go unless we want medals tables and other classifications of sporting achievement to be dominated by All-Star teams drawn from all over the globe, but representing the country with the biggest chequebook.
And, frankly, the more liberal the attitude to changes of sporting allegiance that we adopt, the further down that road - the road to full-scale diplo-doping - we are likely to go, or so it seems to me.
For that reason, I would favour a hard line, significantly harder than sometimes appears to be the case at present, for nationality switches, while advocating maximum flexibility when it comes to the aspiring international's initial choice of country.
That's OK for the base principle.
But the aforementioned complexity and interconnectedness of the modern world would, I suspect, make hard and fast rules difficult to formulate.
Suppose you put a blanket ban on athletes who have already represented one country at elite level from switching to a different nation, as many from the former Stephen Cherono to the former Ahn Hyun-soo, now Viktor Ahn, have done over the years.
Would you then block Kosovo-born footballers who have won many caps for Switzerland in recent times from turning out for their native land now that it has secured governing body FIFA's clearance to play friendly matches under certain conditions, should they wish to do so?
And what about athletes such as Cuba-born triple jumper Yamilé Aldama who marry an individual from a different country and relocate, then seek to represent their new country of residence - would you block them?
Or would you draw the line at athletes who claim to have been frozen out by coaches or managers in their original country's national set-up?
So it is a difficult area to get right.
And that's without even considering whether sports bodies would ever be able to implement their own policies on such a sensitive topic independent of Government.
After all, Governments will always, one imagines, retain the right to grant or withhold national citizenship from immigrants.
Would sports bodies then be willing - or able legally - to exclude citizens from selection for their new country's sports teams on anything other than sporting grounds?
I wonder, under the circumstances, if there is a case for adopting an approach that owes something to the way sport has sought to tackle the admittedly much graver issue of chemical doping, or illicit, performance-enhancing drugs.
That is to say to attempt to draft a standard code that would be applicable across all sports and all national governing bodies, and then use a quasi-judicial chamber to adjudicate specific cases.
Government buy-in would be necessary too, as with the World Anti-Doping Agency (WADA), because of the citizenship question alluded to above.
Perhaps that is going too far; perhaps I am entering sledgehammer-to-crack-a-nut territory.
But I would certainly like to read a worthwhile analysis of the impact and prevalence of nationality switching by elite athletes.
Only then will it be possible to judge whether the phenomenon has reached the point where it warrants a more coordinated response.
David Owen worked for 20 years for the Financial Times in the United States, Canada, France and the UK. He ended his FT career as sports editor after the 2006 World Cup and is now freelancing, including covering the 2008 Beijing Olympics, the 2010 World Cup and London 2012. Owen's Twitter feed can be accessed here.