Breastfeeding is a natural contraceptive.
For agriculture societies however, the planting is easy. Harvest and processing is the challenge. Tendency is to therefore overplant and struggle to harvest it all unless some crop failure or other catastrophe befalls. This keeps you in a pattern to avoid famine but also incentivizing constant population increase to handle harvest.
Now take it a step further and what might you do in times of low food output with excess males? Might be a good time for a war, spend down some of those males and maybe return some more arable land to alleviate food pressure in the remaining population. Maybe the agriculture chiefs of old didn't think in these terms so explicitly, but they are bound by these incentives and history seems to support this sort of model playing out over time.
So you would get higher population growth in Arable societies but not necessarily healthier.