And if you increase immigration, you increase labour supply, and demand for housing - reducing wages and increasing cost of living, which negatively impacts fertility.
The fundamental problem in the USA is the broken healthcare and pension system, which allocates too many resources to baby boomers and unfairly burdens younger workers.
The fertility issue is not a unique American problem. It has been happening for decades in nearly every developed country, and it is consistently observed when populations become more highly educated. The reason it has hit most developed nations harder than the US is because the US historically has much higher immigration rates than other nations, and immigrants tend to skew younger.