Can I just share my belief that this is polite fiction? It's certainly the view of America that we Americans have for ourselves, but can you honestly say you see evidence of it in day-to-day-life - and can you compare it to western Europe?
In my personal experience no, EU migrants are no more marginalized than they are here, and no, American migrants are no more "integrated". Vast swaths of SoCal and Texas is basically Mexico. Huge parts of Florida are basically Cuba. The Somali influx in Minnesota is real and highly separated from the rest of white society there. You don't need to look for ghettos to find large areas of extremely insular immigrants, often 2nd or 3rd generation still with no intention of or interest in immigrating in any sense other than physical location.
I'm not even commenting on if it's a good or bad thing, but ultimately I don't think we've EVER been the melting pot we claim to be, certainly the evidence around us doesn't suggest we are.