This is almost the opposite of what happens.
The more educated/developed a nation, the lesser their birth rate is going to be.
I understand the "shoulds" but that's not what the data suggests.
In essence, we can't have the pie and at the same time eat it.
The most useful thing education does for children is reduce child-mortality rate.[1]
Sources: https://raphael-godefroy.github.io/pdfs/mali_final.pdf
This is misleading. Education is not the panacea. I am saying it's a "whole of family" approach. Governments need to also provide more support to families. This is clear to any parent.
Let us take your previous comment as the basis
> Birth rates would also improve when boys and men are educated.
There is no evidence of this being true. This is certainly a narrative peddled by many ideologues.
> Both genders need education and child support programs.
Poorest of poor and illiterate people happen to have more children than the rest.
> Men/Boys need to understand what responsibilities they have, if they choose to have a child.
If men are educated on responsibilities of alimony and child support, with almost no rights, they would neither marry nor have legitimate children.
> They also need to understand the effects that having a child has on a woman's body.
This maybe your personal dream and that's fine. But this has nothing to do with the topic at hand.
> Governments around the world would benefit their society by investing in family planning, family support (esp. child care) to enable parents to work and provide for their family.
Family-planning is euphemism for reducing children per woman. There's no benefit of having less children -> leading to less economic activity in the future. The family support you keep touting about is moot point. Government does not have their own money. People pay taxes which are used by government.
> An educated and healthy populace (from infant to old age) benefits everyone.
Agreed on this point. The definition of benefits are subjective but overall, it is agreed that it is a net positive.