Pretty much this. It was a huge disappointment for me to understand that even if I made a revolutionary discovery and doubled the yield of food crops, people would reproduce and the prices (and availability) of food would not change.
I don't think food scarcity/availability/price plays any appreciable role in developed nations birth rates but I'd be willing to consider evidence that it does.
I think price is a factor. It isn’t uncommon for someone to say, “another mouth to feed.”
When adding people to a family, food is probably the biggest non-negotiable cost going up.
I’d also expect to see a strong correlation between family size and the percent of meals eaten at home. Going out to eat quickly becomes unaffordable as family size grows.