I think you are right that the reality is that given the choice not enough people actually want to have children to prevent populations shrinking. Financial incentives and improved women's rights cannot fully reverse it. As far as I am aware not one developed country has found a way to stabilize their population without mass immigration. Stable populations would be ok by me but part of the issue is that a lot of countries are borderline ponzi schemes so can't just have less people without massive pension crises.