But we're starting to see it turn around. In the most developed countries, fertility has dropped to replacement or lower. As the remaining countries develop, their fertility rates are also dropping. It's reasonable to extrapolate from this that at some point in the future, the global fertility rate will be at or below replacement.
The constraints are microeconomic. It's expensive to raise children, especially when you factor in opportunity costs (this part is key to why world population won't stabilize at starvation levels). When you give people birth control, people seem to make a rational economic decision about how many children to have. That provides the feedback mechanism you mentioned.