Your argument is that a group of independent states spanning a huge part of a continent that banded together into a country in the 1800s forms a country that is also an ethnicity, but that a group of independent states spanning a huge part of a continent that banded together even longer ago is not a country that is also an ethnicity?
The difference is that - excepting about 1.4% of the population - everyone here in the US is either an immigrant or descended from immigrants. Most of them long after the Mayflower sailed. However long it takes to create a new capital-E Ethnicity, it hasn't been long enough.