Question Author
Seems I have some catching up to do!
Just taking everybody's responses generally, in no particular order:
OK, there seem to be several different shades of the concept here, covering things other than straightforward countries.
Clearly, any place which is named after a geographical feature will necessarily be preceded by the definite article. You could cite these examples endlessly - e.g. the Thames Estuary, the East Indies, the Garden of England, the Balkans, the Arctic Circle, the Benelux, the Pacific Rim, the Eastern Bloc, the Caribbean, the Levant - but I think this is beyond the specific question.
The examples of The United Kingdom and The United States of America are meaningless - this is just linguistically correct, and takes us nowhere.
And I think the whole business of the official names of countries such as 'The Republic of...' is a bit of a red herring, a digression.
For some strange reason, certain countries have always historically been known as 'The...', while others never have, and while there may not be a one-size-fits-all explanation, I believe that there is enough of a commonality between those that have, to make for a useful if small insight into how we came to divide the world up.
The Argentine is an odd one, though.
I still think there is something in my theory of borderless tracts of land up for grabs by our imperialist, colonialist predecessors!
Your further comments please!