For most European and Asian countries, it took over thousand years to form certain cultural stereotypes and cultural paradigms. Back then, people lived in a fairly strict isolation which defined their particular cultural ways and traditions. For a long time, the majority of people couldn’t read or write and legends and fairytales very transferred verbally.

America is a young country, which was formed relatively recently and because of the constant influx of immigrants the nation is not completely formed yet. If this policy would have been curbed, I think American culture would be much more homogeneous.

However, if the current liberal tendency for globalization, open borders, etc. would prevail while the world would change much, and cultural identities between countries would become less and less pronounced.