Immigration and egalitarianism aren't exactly what's keeping us from modifying human embryos en masse. There are ethical concerns that stem from our lack of understanding of many things such as the fact that CRISPR-Cas9 may not be as clean and cut as was once anticipated and may cause mutations in hundreds of genes.
There's also potential backlash from religious groups, Christians and religious people in general still make up a majority of the United States and while the concept of "Playing God" is a largely moot and arguably hypocritical imperative to bring up (Is selective breeding playing God?), any work on the human genome other than curing genetic diseases will most likely face considerable religious backlash.
Also, BPS seems to not understand that birthrates (and death rates) are almost always tied to socio-economics. As countries become more industrialized, they will undergo a sharp increase, stabilization and then a decline in birthrates just as Western Europe and East Asia.