If we were called United States-ians, it wouldn’t really roll off the tongue as well. To the extent that peoples in other countries in the North and South American continents are also members of those continents, they can reasonably call themselves “North Americans” and “South Americans” in the same way that other people around the world call themselves “Europeans”, “Africans”, “Asians”, and “Australians”. Though no one really calls themselves after multi-continent land masses; “Eurasians” isn’t a popular rallying cry despite the existence of Russia and Turkey. Calling people from the USA “Americans” is simply a useful, easy-to-pronounce shorthand for “people from the United States of America”. And, to be fair, the USA is the only country in North or South America to also have the word “America” in its name.