"American" might come from the fact that the name of the country is the United States of America. People are normally referred to by the name of the country; Spanish people in Spain, English people in England, etc. Calling the people "United States of Americans" is too much of a mouthful and is terribly unclear. Perhaps the question should be about what the country is named instead of what the people are called. Taken literally as a description rather than as a name, "United States of America" would refer a union of all the governments in the Americas. But since it is a name and not a description, calling the inhabitants "Americans" makes perfect sense.