If the citizens of other countries in the Western hemisphere want to use the term for themselves as well who cares? So be it. Have fun! (Going by the "North" and "South" logic there would be 3 of them.. There are several countries in "Central America" too!

)
But the whole thing is pretty trivial. "Americans" as applied to the US is something that WE were labeld by the Europeans just like the trem "Yanks". It isn't something that was generated on this side of the ocean.
You used the term "Brits". Why is the term used by/about the people of Great Britan? Aren't the people of Brittany, France "Brits" too?