This isn't an over-generalization of the founders intent. It is the founders directly, clearly stated intent. I'm doing literally no extrapolation at all: you can just crack open Federalist 52 or whatever and read away.

Here is Federalist 52: https://avalon.law.yale.edu/18th_century/fed52.asp

Show me where it says there is a moral obligation to accept immigrants who will move into your community and change its culture? You’re reading all that into a single sentence:

“A representative of the United States must be of the age of twenty-five years; must have been seven years a citizen of the United States; must, at the time of his election, be an inhabitant of the State he is to represent; and, during the time of his service, must be in no office under the United States. Under these reasonable limitations, the door of this part of the federal government is open to merit of every description, whether native or adoptive, whether young or old, and without regard to poverty or wealth, or to any particular profession of religious faith.”

The sentence is saying that elected office should be broadly available to all citizens, which is a point nobody is disputing.

Ironically, the INS Act of 1965 was sold to the public with a lie: https://www.history.com/news/immigration-act-1965-changes

> The bill will not flood our cities with immigrants,” lead supporter Sen. Edward “Ted” Kennedy (D-Mass.) told the Senate during debate. “It will not upset the ethnic mix of our society. It will not relax the standards of admission. It will not cause American workers to lose their jobs.”