> Human change can be subject to the law of large numbers, but nothing necessitates any particular change being towards progress.

The same can be said of the "Great Man Theory" (or its adaptation by selecting immigrants based on some selected set of skills). You don't know that you're making society better, you're just selecting for a certain set of skills.

> The American melting pot works well (or worked well) because it was a nation made up from a blank canvas with no prior historically established dominant ethnicity or culture the kind other nations have had going for millenia.

This isn't true and it ignores the cultural differences amongst all of the original colonists (religious, language, political, and country of origin). That's before you even consider the stark differences in culture between the Native Americans and the European colonist.