The effect of population controls would probably have to be designed to be more of a band-aid than a cure. For example, we can make it so that population controls create significant unrest and/or neighboring countires are more likely to intervene. And then this unrest makes the implementation of population controls more difficult. Maybe population controls works for some time, then unrest makes the policy ineffective. Then the planet ends up in the evitable situation -- overpopulated. We just delayed it. To have the system I proposed work with the idea of population controls means that we have to think of how we can design population controls weak enough to make expansion inevitable, but still be strong enough to be an effective delayer.