I doubt many of the writers really care whether the uk or us would actually survive into that time period.
Though you do make me curious, as I don't off the top of my head recall anything other than the British flag in STID that suggested either country really survived beyond the 21st century. What kind of examples are you thinking of?
Kirk is from Iowa, Riker is from Alaska, Janeway is from Bloomington, Indiana. The United States exists at least as far as geography is concerned.
Picard is from France, so there is another country explicitly mentioned by name. Canada was also mentioned.