When I was young, the "melting pot" was the dominant metaphor for America vis a vis immigration. Of course, that was during the period between 1923 or so and 1965 when immigration was basically restricted to Western Europe. (Mexicans were "wetbacks" or migrant workers, not immigrants we recognized.) The idea I took away was like melting your crayons all together, which I'd done once or twice.
In college a young government professor named Theodore Lowi, who later became prominent in the political science field, suggested maybe the better metaphor was "tossed salad". Rather than the different nationalitiies all melting together and forming a new American nationality, each one would maintain some of their identity. That would logically lead to the "diversity" argument; the theory that America prospers by recognizing and maintaining differences.
The above is just background. In recent years I've grown interested in genealogy. Some of my paternal ancestors came to America in the 1720's or so; others came in the 1820's. What seems to be the case is they were almost entirely Scots-Irish, Covenanters. The exception is a Quaker lineage. And, through geographic concentration and cultural networks (the Presbyterian church), my ancestors seem to have kept together, marrying within the general Scots-Irish community, for about 200 years of life in America. Even in my father's generation his brother continued the pattern.
Because my mother's ancestors were Germans emigrating in the last half of the 19th century the picture is not as distinct, but my maternal grandparents married within the German community.
So, at least based on my limited sample, it's true enough the "melting pot" metaphor is misleading. Yes, we eventually melt together but it takes a long time. And even the melting of Scots-Irish and German is not the merging of polar opposites. Lutherans and Calvinists have different theologies, but they aren't polar opposites.