The test we should do is to try is searching some European newspapers and see if they ever say "Berlin, Germany" or "Brest, France" or "Copenhagen, Denmark". Or if you ever see "Shanghai, China" in a British paper. I don't think we would. It's definitely an American (and Canadian!) format which, when applied to the rest of the world, has the effect I described.
There are two parts to your argument.
1 - Americans (and now Canadians) are unique in that they reference their own cities qualified with a named sections (e.g. states) of their country.
2 - Americans extended that behavior to foreign references because they had that habit with local references.
For 1, I did look for other examples, but Europeans referencing European cities is not one I'd look for. Rather, I would have to find single countries, with many named regions, where the citizens use those region names to qualify their own city names. I had language and paywall problems when looking up foreign newspapers. I suppose good candidates would be China, Mexico, and India; you gotta have a big country.
For 2, I think our pattern can be explained. The US and Canada are quite geographically isolated from the rest of the world. When our habits developed, we probably saw the world as "our continent and everything else". I guess, we kind of still do; you guys are so far away. It's kind of like, when you're way up in a spaceship, countries do look like little states.
An interesting question, which I'll leave up to the therapists to answer, is why some consider this useful pattern to be crass and patronizing. When I hear "Brest", I think of Belarus. (My grandmother was from there.) Adding the country really does help.
"Dudley!!! Can you believe that stinkin' American! Pass me another pint and join in the mockery."
"Easy there Nigel. Take a deep breath and consider their point of view. I think I'll have to call your mother."