They didn't manage not to beget children. A number of those single women tossed their newborn into the river or gave them away because a single woman with a child couldn't get work.
And there were both birth control and abortions. They were not advertised but every girl knew who to go to if she "got into trouble". Paying for it was another story.
And there were a lot of illegitimate children then as well. 75% of the births in St Giles were out of wedlock.
But your point of you get more of what you subsidize is taken.
I can see that you got my over-all point: you get from people what you expect from them, for the most part. And a society that fully expects people to screw around like crazy and not even bother with birth control, or avail themselves of the "choice" that they so diefy, will have an ever-increasing supply of feral children who need feeding until they are big enough to rob you on their own.