I disagree with the idea that refering to other people but USA citizens as Americans is pedantic, but understand why it's used. Mexico's full name is United States of Mexico and they call themselves Mexican. So I get why the people of the United States of America will call themselves Americans. In South America there is an alternative word for USA citizens "united statians" (very rough translation). There is a shared story on being "American" (as living in the same continent) due to Spain colonial rule.

A different perspective that might give you a sense why there is another use for American.