> According to the quote in the OP the locations do change over time.
> Maybe the post office or whatever they use as the official center
> changes, I don't know.

Quite possible.  And even if Rome doesn't move, it does change ;
whether they use the post office, centre of the postal district,
centre of population, or even someone's guess, coordinates are all
subject to change, agreed.   Shifts of 1km would be of no real
consequence inside a large city.   Shifts of 40m are rather
meaningless regarding the location of a city, or even a village.

I think that means it's a bad idea to store the coordinates only, and
then later on to geocode a query like 'Rome' and then go on to see if
the coordinates can be matched exactly.
You'd need another approach, like seaching your database for the text
'Rome', or 'Italy' or 'Sweden'.
Or you might search for coordinates within some distance of the
target.
Or you might store polygons represent the city or country in your
database, and see if a query target point falls within them.     But
then it would be difficult to determine if you should match on 'Rome'
or 'Italy'.

It's difficult to advise further without knowing what you're trying to
accomplish.

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