Why didn't you try to look at some numbers? If anything, immigration to the US has accelerated in the last 50 years. 4.7 percent of the population were immigrants in 1970. The number increased to 13.7 percent in 2019.
"Since 1970, the share and number of immigrants have increased rapidly, mainly because of large-scale immigration from Latin America and Asia. The vast diversification of immigration flows was ushered in by important shifts in U.S. immigration law (including the Immigration and Nationality Act of 1965 which abolished national-origin admission quotas; the creation of a formal refugee resettlement program with the Refugee Act of 1980; and the Cold War-era grant of preferential treatment to Cuban immigrants); the United States’ growing economic and military presence in Asia and Latin America; economic ties, social linkages, and deep migration history between the United States and its southern neighbors; and major economic transformations and political instability in countries around the world." - [0]
People from Asia and Latin America, those who contribute the majority of the boom in migration since 1970s, are those by default don't speak English natively and have distinct culture. 22 percent American spoke a language other than English at home.
> Modern US cities are not capable to accept and absorb large scale immigration of people who are not already integrated into society. People who do not speak local language and have very different culture.
Incorrect. As of 2018, 20% of NYC residents are naturalized citizens (born abroad), 10.9% are legal and 6.3% are undocumented immigrants. [1]
[0] - https://www.migrationpolicy.org/article/frequently-requested...
[1] - https://www1.nyc.gov/assets/immigrants/downloads/pdf/moia_an...