I grew up in a place where there was great diversity of origin among the population; various areas of the State were settled by people from all over the world.
Many of these people spoke their native language at home and kept the cultural traditions of their countries of origin. BUT, they also assimilated into the American culture and ethos, becoming part of the great melting pot which is the US.
Without that assimilation, we would not have many of the cultural features that make us uniquely American. There would be no R & B, no Rock n Roll, no Rodeo, no Barbeque, no gumbo, no Cajun music, no Zydeco, no Tejano, no Country music, no Western Swing, no Bluegrass.
Only in America could a native speaker of German command a navy at war with Germany. [Adm. Chester Nimitz] Only in America could a native speaker of Japanese receive the highest military honors while serving in an army at war with Japan [Sadao Munemori].
I could go on forever, but I can make a very valid argument that the strength of the American Culture is not Diversity at all; it is the chaotic and innovative assimilation of originally diverse people and cultures into something that is both the same and wonderfully different from any other place in the world.
In a single sentence: We invited anyone to come here [legally] NOT to be who they were before, but to be joyously welcomed to become one of us.