I don't see how the numbers support that claim.
What percentage of the population would you like to see made up of immigrants? Would you make immigration harder if the immigrant populating was above 1%?
If it got too high, would you start deporting people or forcing native people to have more children?
According to a 2021 Cato survey--which is a pro-immigration outfit--the median response to "how many immigrants should be allowed each year" was 500,000: https://www.cato.org/sites/cato.org/files/styles/aside_3x/pu.... If we enforced that number long term, we'd probably end up with a foreign-born population under 5%, as we had in 1970. That seems like an appropriate number to foster cultural homogeneity and a high level of social cohesion.