The Hitch Solution to Poverty

I happened upon 24 minutes of Christopher Hitchens at his marvelous best. In minute 2:15 (to 2:52), Hitch expresses his theory for the solution to poverty:
Mother Theresa, is endlessly praised for her work, that most of the time she never did, I went to watch her very closely in Calcutta. You don't mind that she thinks that what Bengal and Calcutta mainly needs is a clerical campaign against birth control and family planning. Has anyone ever been to Bengal and Calcutta and concluded that's what it really needs? That's what she's really campaigning for, in case you're worried. But never mind, she gives a wonderful impression of being a charitable person. So what Indians need is more missionaries, to cure poverty, when everyone knows there is only one cure for poverty which is the empowerment of women, which means giving them some sort of control over their reproduction --- much applause.
I take the spontaneous applause as a pretty good indication that many in the audience agreed, that ... everyone knows there is only one cure for poverty which is the empowerment of women, which means giving them some sort of control over their reproduction ... I applaud also.

I'd certainly agree that the missionary position is a sure path to poverty, the empirical evidence is clear on that. Religion has been around a long time, it has always promoted population growth and the result has been perpetual poverty. If they really wanted to prevent poverty, you'd think that they might have learned something by now. Two possibilities come to mind:

But, Hitch was the first to admit that a scientist he was not. The scientist in me wonders what is the empirical evidence and how does the Hitch theory relate to other theories? We do know that the poorest nations also have high fertility. We do know that some women, in some cultures, reduce their fertility to replacement or less when given reasonable access to contraception.

It seems pretty clear that ...giving ... [women] ... control over their reproduction is a necessary condition for overcoming poverty, but is it a sufficient condition?

Consider a population which generally reduces its fertility but contains within it a coherent subset that persists with high fertility. The total population may at first appear to stabilize (or even decline) due to the majority reducing their fertility but in the long run the high fertility group will dominate and population will soar higher than ever. The historical record is clear, religion is one mechanism that has demonstrated long-term maintenance of a coherent cohort of selfish breeders. (Religions have a long track record of genocide, this would add reproductive genocide to the list religious achievements.) Are there other mechanisms?

It seems that we also have to do something about religions in order to solve the poverty problem.