It was also a time when immigration laws were enforced, and new arrivals could not live off free US government benefits while not paying taxes, hording their cash, and sending it out of the country.
This is exactly correct.
I think it was the conservative writer John O'Sullivan who, several years ago, said something like this: If you will abolish the welfare state and rescind the doctrine of multiculturalism, I will withdraw my objection to large-scale immigration.
Even under those conditions, however, I would still take offense at the illegal variety of "immigration"--more precisely, a bloodless invasion.
You lost me here. In reality, most southern and eastern European immigrants lived in self-segregated ghettoes (many of which remained for three generations). Most came solely for economic opportunity (not to "become American: whatever that means) and many initially came here with the idea of staying temporarily.
The attitude of the elite back then was, essentially, "we don't care as long as they don't overthrow the government or move into our areas." The attitude of the masses was negative, which is why the KKK had its peak years of membership from 1900-1925, when it was an explicity anti-immigrant organization.
The concept of the "melting pot" was actually an idea proposed by American liberals, as an alternative to the "cultural exclusionism" favored by the Right at that time. It never really was true, it took 3 generations for eastern/southern Europeans to fully assimilate (and become largely indistinct from other white Americans in terms of behavior and social mores), while blacks and Asians were not part of the "we" of the melting pot (even the liberals back then had their racial issues).
What we really need is enforcement of current immigration laws, an inculcation of constitutional principles among both the native born and the immigrants, as well as (dare I say?) a more inclusive sense of "we." That's my 2 pennies FWIW.