In such cases, the birth rate should actually rise.

Why does it grow? Now almost in all countries is a situation when the carriers of good genetics refuse to give birth to offspring (not all yet, but already a decent number). While people who are not burdened with moral values are very active.
It is bad for society. It is normal for evolution. Humanity makes a leap back in development as a result of too many egoists. Per in the next round of evolution there will be more people caring for universal offspring, and humanity will take another step in development.
Maybe he will die. The universe blows.