Here's some cool census data on trends in the foreign-born population of the United States. Two things pop out—one is that we're not at the sustained peak levels we had between the Civil War and World War I. The second is that the 1950s and 1960s that American liberals often cite as halcyon days for the economy were near the immigration nadir.
Your mileage may vary on that latter fact, but my interpretation of it is that it gives reason for less hoary nostalgia about those days. For one thing it's just a sign that the postwar United States was not a "land of opportunity" in the way it is now and was earlier for people born in foreign countries. The American mythos of upward mobility has always had a lot to do with the immigrant experience. The first generation gains some new opportunities by moving to a richer and freer country but is naturally held back by a lack of language skills and relevant local connections. The second and third generations are less held back by those factors and are able to obtain a much higher level of prosperity than they would have if their parents and grandparents had stayed in Poland or Mexico.
But the other thing is to remember that the presence of foreign-born people skews a lot of statistics. The foreign-born population in the United States is poorer than the native-born population. If all those people evaporated tomorrow, the average income of the remaining people would fall but per capita income would rise due to compositional effects. We would also have "more equality" since a disproportionate share of the poorest people would have vanished, and the incomes of capital owners would fall more than the incomes of wage earners. But again, very few actual people would be made better off this way. The better way to get the poverty-reducing effects of eliminating the immigrants is to simply count income per natural instead. The average income of people born in Mexico is higher than the average income of people residing in Mexico, because many of the people born in Mexico now live in the United States. Conversely, the average income of people born in the United States is higher than the average income of people residing in the United States, because many of the people residing in the United States were born in Mexico.