The best available evidence is that fertility rates are highly sensitive to external incentives. For example Russia managed to raise its fertility rate from the lowest in Europe to one of the highest in just a decade. They did that through a combination of cash incentives, extended maternity leave, and various social status and privileges for mothers.
The only way it is beneficial is because some jokers decided that running country on ever increasing debt (esp. retirement) is acceptable, and another decided that growth rates have to be high.
So the biological urge apparently isn't doing the trick.
While that may end up being the case for centuries to come, I don't think it's a great outcome for humanity as a whole to require vast wealth inequality between nations in order to keep humanity from dying out.
I raise you Israel as an example of not a poor country with big increase in birth rates.
It's really not like military service or jury duty: things which in most cases people do not have an extremely strong biological urge to do.