Yes, the point above about the name of our nation being the United States of America is the best explanation for why Americans came to be known as Americans. People are named according to the name of their nations when referring to those nations and the unwieldiness of "U.S. Americans" seems unnecessary.

And how very, very sad it is to read from Bel' that Americans travel with the flag of another nation on their luggage. I will struggle with this knowlege all the night long...