Its usage hundreds of years ago inside the US, yes. That's a pretty irrelevant argument for the rest of the remaining countries that are part of America, isn't it?

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...