Regina, Saskatchewan; Canada
Yes it does bother me as being a misnomer, because it would be like people using the word European specifically to mean "French" instead of "European". It may be popular, but that does not mean I won't avoid it and encourage others to avoid it. United Stative is a good alternative to such a popular misnomer.
If you look at how the word continent was originally used more loosely you will see how the whole new world was seen as one "America", the "America", the continent, that is referred to in the name of your country. It was not pluralized as "Americas" and it is still not always pluralized even today when they are considered together as a whole.
"The word continent
From the 1500s the English noun continent was derived from the term continent land, meaning continuous or connected land and translated from the Latin terra continens. The noun was used to mean "a connected or continuous tract of land" or mainland. It was not applied only to very large areas of land — in the 1600s, references were made to the continents (or mainlands) of Kent, Ireland and Wales and in 1745 to Sumatra. The word continent was used in translating Greek and Latin writings about the three "parts" of the world, although in the original languages no word of exactly the same meaning as continent was used.
While continent was used on the one hand for relatively small areas of continuous land, on the other hand geographers again raised Herodotus’s query about why a single large landmass should be divided into separate continents. In the mid 1600s Peter Heylin wrote in his Cosmographie that "A Continent is a great quantity of Land, not separated by any Sea from the rest of the World, as the whole Continent of Europe, Asia, Africa." In 1727 Ephraim Chambers wrote in his Cyclopædia, "The world is ordinarily divided into two grand continents: the old and the new." And in his 1752 atlas, Emanuel Bowen defined a continent as "a large space of dry land comprehending many countries all joined together, without any separation by water. Thus Europe, Asia, and Africa is one great continent, as America is another." However, the old idea of Europe, Asia and Africa as "parts" of the world ultimately persisted with these being regarded as separate continents.