If the desire to have children has a genetic component, and those with this genetic component are more likely to have offspring that survive until adulthood, th

If the desire to have children has a genetic component, and those with this genetic component are more likely to have offspring that survive until adulthood, then the trait will spread. Given that plenty of heritable traits (like religiosity) are correlated with increased brood size, I'd say it's pretty likely. Also, given that in first world countries even the offspring of poorer folks survive to adulthood, that removes any benefit of giving birth to fewer children.