As KHorton has alluded to, there is a well-established body of literature which indicates that development leads lower Total Fertility Rates. Examples include the books Common Wealth by Jeffrey Sachs and Factfulness by Hans Rosling et al. The following online resources also explore this:
- This article indicates that meeting the UN's SDGs would lead to lower population growth https://www.pnas.org/content/early/2016/11/28/1611386113
- David Roodman has explored this point at GiveWell's encouragement: https://davidroodman.com/blog/2014/04/16/the-mortality-fertility-link/
- Giving What We Can has also written about it: https://www.givingwhatwecan.org/post/2015/09/development-population-growth-and-mortality-fertility-link/
The global fertility rate has halved in the last 50 years, so I don't think this is as much of a problem as you suggest. Our World in Data attributes the decrease in fertility rates to increasing women's empowerment and decreasing child mortality. https://ourworldindata.org/fertility-rate
I'll also note that poverty rates are declining sharply in most of the world's poorest regions, which makes the "bottomless well of help" claim seem a lot weaker.
thanks to you both, that looks pretty convincing