What is the reason for population control in "By the Waters of Babylon?"
There is not a lot of population control in "By the Waters of Babylon." That is not the main point of the story. The population control that exists is written about in the very beginning of the story, and it stems mainly from superstitions and tradition.
It is there that spirits live, and demons . . . —they have been forbidden since the beginning of time.
Don't go east, because that's where the evil demons live. It has been like that forever. It hasn't actually been since the beginning of time. Those rules have been in place since "The Great Burning." That is likely some kind of nuclear holocaust that killed off millions of people.
The basic rules of the population control are simple. Don't go east. Don't go to the Place of the Gods. Don't go to the Dead Places. Don't touch metal. The reason those rules are there is to protect the lives of the people. Assume that a nuclear detonation did occur over New York City (Place of the Gods). There would be radiation there for decades and decades. Going east would be going toward the contaminated city, and radiation poisoning would kill people. The population control exists to save people's lives.