Agreed. However this is something that most of the world (aside from Mexico, Central, and South America) collude in. I try to say "the US" in conversations with my European friends, but they will always just say "America" in response. And of course, there is no English equivalent to Estadounidense.
The French language has "États-Unien" [0] but it is almost never used.
Of course, even that _could_ be ambiguous given that my homeland's southern neighbor is officially "Estados Unidos Mexicanos" (Mexican United States). That usage is so rare as to be pretty much irrelevant, though.