(Sorry, but the Americas is what the continents are called normally - in English at least - did you just make up a new rule? There's even a Wikipedia entry: https://en.m.wikipedia.org/wiki/Americas)
Regardless, the name for Americans isn't changing any time soon, so I wouldn't get worked up about it. Besides, we are Americans in the most pedantic use of the term - if the Canadians, Mexicans and anyone else in this hemisphere wants to call themselves Americans too, they can go right ahead. They'll just seem petty and silly though.
No, the continent(s) have traditionally been called America. A look at Google Ngram Viewer shows that Americas has hardly been used. It's a recent phenomenon, probably a result of the US hijacking "America". Even I feel sometimes compelled to call it "Americas" in Europe because it has become a given that US=America.
Not sure about the literature of the US, but in Latin American literature, writers have generally referred to the continent(s) as America, e.g http://www.historyofcuba.com/history/marti/America.htm
The original map by Waldseemüller has "America" written on it: https://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Wa...
To me it's similar to the demonym 'New Yorker'. Is that someone from Buffalo, Schenectady, etc., New York or from the five boroughs or from the county of New York, ie, Manhattan?
What about Netherlander instead of Dutch since it's a corruption of Deutsch. We could go on about makes sense and what doesn't.
> It's no different than if the most powerful European country were to call themselves Europeans alone.
Assuming always that it had established itself as the Federal Republic of Europe or some such before anybody else claimed the name.
Abroad, Hollywood has popularized the use of "American" to refer to citizens of the USA. Also, most languages don't have any other way to refer to US citizens because of its odd name. I'm only aware of Spanish "estadounidenses".
It's no different than if the most powerful European country were to call themselves Europeans alone.