The U.S. Melting Pot has one big thing that these other countries lack: a lack of history. People in the US are not resistant to their immigrant compatriots adoptiong American culture, and in fact readily share it. Most European countries like Italy, Greece, France, and so on, have a hidden yet obvious nationalistic bias tied to heritage. In France or Italy, you will never become a true Frenchman/Italian as an immigrant even if you adopt their culture, whereas in America, the Indian who Americanizes him/herself is applauded rather than shunned.
In Europe, ethnicity is closely tied to nationalism, and the borders are drawn accordingly. That is not the case in the US because the only native ethnicity available is one that was sadly wiped out.