Part of the problem I think, is that The United States of America, much like The Dominican Republic, suffers from Clunky Name Syndrome.
Consider Spain, for example, simple and elegant. ?Where are you from?? ?I?m from Spain.? No Problem. The formal name of that country is not Spain however; it?s the Kingdom of Spain. But people being naturally lazy, no one ever says ?I?m from the Kingdom of Spain?. Instead they just say Spain.
Likewise, if someone is from The United States of America and is asked where they are from, it is much easier to say America or The States, than to labor through all those tedious syllables. And therein lays the problem.
The United States of America seems to be about the only country that decided to include the name of its entire continent (or continents) in its formal title. Had Truth in Advertising laws been in effect in 1789, the name would probably be something like The United States of Central North America. And that would be even more of a mouthful, so we?d still say we?re from America and annoy people who care about such things.
NALS has pointed out that there is also another United States (of Mexico), so my choice of response when asked where I am from would be The USA.I think that gets the message across and is also easy on the tongue.
BTW, to be fair to my homeland, I would like to point out that we did not usurp the title America, we just used it. Any other country in the hemisphere was free to follow suit; viz: The Republic of America; The Kingdom of America; The Disunited States of America, etc.