Well the birth rate is barely at replacement level already in many of the wealthier countries (and actually below it in some countries).
Link to birth rates by country.
So what you seem to be advocating is for the couples from the wealthiest countries to stop having children of their own, and instead adopt some of the excess babies from the 3rd world. This is not only unlikely (as the majority of couples who want to be parents want to have their own child), but doesn't really solve the overpopulation problem.