China's one child policy is a real example of state population control that isn't horrific, though criminals trying to get around it have done horrifying things. Licenses for having children have been explored in numerous novels, with the downsides usually similar to the OCP.
Did you actually looked how the Chinease fertility developed?
The thing the one child policy achieved is that the rapidly declining fertility stabilized and showed a minor temporary increase. Net effect: a few tens of millions of extra kids are born whom would not be born without the one child policy (not that it was a bad thing in the long run, without the one child policy China would had serious workforce shortages a decade earlier).
BTW this graph also shows a more greater danger than overpopulation, once an economy reaches a high enough sophistication then raising a new generation of workers will be beyond the capabilities of the given economy. It would be an interesting endgame disaster that overly costly educational system leading to a population collapse for a given empire and they have a constant need to acquire new citizens (by peaceful immigration or abduction) in order to maintain their economy.