I agree that we really have no idea who fought in WW III. We know that there was the Eastern Coalition, i.e. China (according to the commentary for ST:FC), but as for the other powers, it could be anybody. There's no indication that the US would have been blitzed to smithereens or anything like that.
Indeed, we know the USA survived WW III basically intact, as the war took place in 2053 but (in TNG's "The Royale") a 52-star flag is said to date back anywhere from 2033 to 2079...and also there were U.S. addresses given from time to time in Enterprise
. Plus, we've seen major U.S. cities like San Francisco several times in Trek. And Trip Tucker has been to New York City. (We all know what kind of war WW III must have been...a total nuke war, it would wipe out everything. And it would take several centuries to rebuild a city completely from scratch, so if we see a city anywhere in Trek, we can realistically assume it survived the war, because otherwise there would be nowhere near enough time to totally rebuild it.)