People have been immigrating to the Americas since its discovery. The actual natives to this country, in fact, have been almost fully extinguished by European immigrants and are now largely relegated to reservations on the least-desirable places in the country.
They are the ones who are poor and bereft; and their culture is practically extinct. So, don't lecture anyone, especially someone well-educated in American history, about how immigration can change a place.
Nevertheless, modern immigration doesn't change a place that dramatically and for the worse, especially when it's controlled. If you read your history, you'd know that every wave of immigrants to this country has been met with fear, contempt, and opposition (including my family's, as starving Jews escaping the Third Reich). Yet, in the long term, the feared outcomes--similar to the ones you describe--never came to pass. America doesn't look like Italy. It doesn't look like Ireland. It doesn't look like Israel. It doesn't look like Mexico. It doesn't look like Vietnam. It doesn't look like India. Maybe certain neighborhoods do for a while, but that's actually one of the nice things about America: that you can go spend some time and enjoy the fruits of a different culture without leaving home. Yet they're still subject to American laws, regulations, and supervision.
And immigrants don't get to vote, so they don't have much political influence for a long while, even locally. Remember, too, that it takes a supermajority to amend the Constitution, so for immigrant culture to have a serious impact on the USA itself would take generations, to the extent it ever does.
I never suggested that immigration should be entirely unregulated and that people and cultures are fungible. That's a straw man you created. And the fact that you are assuming that's the situation people want and the inevitable outcome that will result reveals who you are, and yeah, I'm going to fucking moralize on it. Racists and fearmongerers are evil, even those who hate their own kind. Your own argument supposes that morals are a part of transplantable culture, and let me tell you: Racism, fear, absolutism, and contempt for outsiders are not American values. Perhaps you need to work better on assimilation, yourself.