Immigrants may become legally American overnight, but they don't become culturally American overnight. Cultural attitudes are extrmely durable (https://www.sup.org/books/economics-and-finance/culture-tran...). My mom has lived here for 36 years, and she's still a low-social-trust south asian who has distinctly south asian views on credentialism, education, social hierarchy, etc. Are those attitudes compatible with the kind of egalitarian, self-governed democracy Alexis de Tocqueville wrote about? I am skeptical that's true at scale.
Even having grown up here, my cultural attitudes are very different--and again, distinctly south asian--compared to my wife's (whose family has been here since the early 1700s). If you took 1,000 people like my wife and put them on an island, you'd recreate America--including the parts of America I find perplexing and frustrating. I'm not persuaded that if you took 1,000 people like me and put them on an island you'd recreate America.