Improved quality of life and reduced infant mortality are shown to reduce population growth by creating incentives for people to have fewer children. If you want fewer people, then you want to improve the material well-being if as many people as possible. As it stands, the global population is projected to peak at around 10 billion people some time this century, per current trends.
I think this is incomplete. In every case so far a reduction of infant mortality and improved quality of life are coupled with power structures that increase the amount of productive output that is captured by a family, increasing the relative cost of producing children.
I don't doubt that wealth can be a factor, but those systems are a whole lot more complicated than that. Money+Low Gini = Low birthrate is a meme as much as it is a primary driver.
