We were on the Europe wise scale---which pretty much was the World back then. Or the part which mattered at least.It's particularly terrible in HoI 3, a game where America is one of the most important powers. Also, Denmark was not influential "on a world scale" in the 1400s. Nobody really was.
Can't remember how the province setup is in HOI3, but I agree that countries like the US should have a focus on being correct in the HOI series.