A very interesting question. The answer, I suppose, has to do with the wealth, power, influence and international profile of the USA. The lack of exact demonym can cause problems, especially for those who want to be precise and not cause offence to the millions of people who live on both American continents who are not US citizens. The vast majority of the non-US citizens of the American continents are Spanish-speakers, and there is a word meaning 'Unitedstatian' in Spanish - it's 'estadounidense'. Unfortunately, there is no equivalent word in English. The only more precise term is 'US citizen'.

You say someone is a North American if they are from the North American continent and a South American if they are from the southern continent. Hence both Americans and Canadians are North Americans but people from South America are South Americans. :)

Hahaha I don't know why there isn't a word like that. We even call ourselves Americans. :)