It seems like people being able to reproduce at-will would be the problem. Designing a system where people are sterile by default and can only have a child with

It seems like people being able to reproduce at-will would be the problem. Designing a system where people are sterile by default and can only have a child with intervention seems the only way to prevent random population explosions. If some group in your population finds religion and decides to be fruitful, you have a big problem. If 15% of your population has double replacement numbers, you have a 45% increase in your population in two generations.