I understand that “real world statistics” don’t really combine well with socialism, but do consider the fact that countries which meet all of your first 3 criteria (higher birth safety, lower medical expenses, paid maternity leave) have a LOWER birth rate than the US, generally speaking. Some examples are: Norway, Germany, UK, Denmark, Italy, Spain, the Netherlands and the EU average.

The best determinant as far as high birth rates go are (and I say this as someone who is pro-abortion up to 9 months, always uses birth control, anti kids dying and atheist):

a. Child mortality

b. Participation in a pro-brithgiving religious community (e.g. Catholics, Muslims, various Evangelic cults, etc)

c. Lack of access to a abortion and birth control

And, arguably, b. c. can be confounded by a. (since lower child mortality is associated with prosperity which is in turn associated with access to birth control and general loss of religion).

Anything else is pure noise, kids are mostly “spur of the moment” type things, few people plan for them, the kind of people that do plan carefully are the kind that have a health insurance and savings to care for the kids anyway.