What you're arguing here is largely ahistorical. Immigration to the US was relatively small scale and almost entirely from highly compatible cultures. There's a decent write up here [1]. Some datums: Immigrants today (including illegal) are about 14.3% of the population - that's about the same level as it was following the great migration of the late 19th century shortly before it started to become an issue leading to immigration being clamped down on hard, reaching a low of 4.7% in 1970. [1]
Fertility, when shared amongst a population, has an easy to model effect on population. It's a population scalar of fertility_rate/2 per ~20 years. So a fertility rate of 1 would mean your population is dropping by 50% every 20 years. That is compounding/exponential and never ends until you go extinct or start having more babies. Compensating for this by immigration is basically impossible, and at that scale you will quickly become the country of origin of immigrants in any case. Of course we're not even especially close to a fertility rate of 1 yet, but that is the trendline and really the same argument even applies to rather higher levels of fertility.
Fertility, when shared amongst a population, has an easy to model effect on population. It's a population scalar of fertility_rate/2 per ~20 years. So a fertility rate of 1 would mean your population is dropping by 50% every 20 years. That is compounding/exponential and never ends until you go extinct or start having more babies. Compensating for this by immigration is basically impossible, and at that scale you will quickly become the country of origin of immigrants in any case. Of course we're not even especially close to a fertility rate of 1 yet, but that is the trendline and really the same argument even applies to rather higher levels of fertility.
[1] - https://www.pewresearch.org/short-reads/2024/09/27/key-findi...