> America has had almost no assimilation of immigrants into the cultures which existed there before

That's almost a uniquely United States problem, not at all as big of an issue in most of the Americas. Only a few countries in the Americas have had their native population pretty much entirely wiped out without any assimilation whatsoever. The US is one of these few countries (Cuba and Hispaniola would be other examples of total replacement).

The rest has had large degree of intermixing or wholesale population preservation. Aspects of native culture is those countries were suppressed historically but are still preserved in some way to this day.

It's also very fair to say sovereign countries today can build a healthier immigration policy than 1500s Europeans with their extermination campaigns. I'd be the last to say that is an example to be followed.

More to the point here: Japan can be exclusively Japanese for another 200 years and die forever, or be Japanese + something for another 10 thousand years. Unlike 500 years ago, they get a choice.