You also don't seem to notice the contradiction between maintaining on the one hand that an increase in wealth reduces population and that subsidies to mothers increases population. Surely a women with more income has more choices than one with less. If more choices is supposed to by itself lead to fewer children then handing out checks on the street corner would reduce population. It doesn't.
Because the fact of the matter is, the relation between wealth and population is entirely contingent and not at all necessary. It is a matter of the free choices lots of people make. Historically, rising wealth went hand in hand with exploding population - for a while. Then with decline population growth, and now finally with overall demographic decline (which is just begining and so far nobody knows how large it will become before reversing).
Of course extra choices for emancipated women go hand in hand with increased societal wealth. First because the wealth funds the labor saving devices that reduced domestic work to a minor afterthought, and second going the other way because women added to the labor force increase societal wealth.
As for whether people are too stupid to use birth control properly, it would appear the middle class and wealthy are stupid enough to over-use it to the point of demographic suicide. So who is stupid? Is it stupid to have a large family and thus less wealth per capita? Or to have none, and leave a demographic wasteland for foreigners to inherit after all one's own offspring have disappeared from the face of the earth?
Again, this is exactly my point. There is an assumption being made that what the rich are doing with their reproductive freedom is sensible and the poor are stupid not to do the same things. When in fact what the rich are doing with their reproductive freedom is stark raving mad and unsustainable, headed right off a cliff, and forcing the poor to do it too would hardly help matters.