For governments to completely control birth rates via artificial wombs/artificial births, they'd also need to neuter/spay the human population to prevent natura

For governments to completely control birth rates via artificial wombs/artificial births, they'd also need to neuter/spay the human population to prevent natural births. This would be simple for children of artificial births as the government could spay/neuter them at birth. But how would a government spay/neuter the naturally born population? Government handouts, tax incentives, compulsion? Get spayed/neutered for 20 years of no income tax? If we were to go the artificial wombs route, then human sexuality/desire/etc would no longer be needed and spaying/neutering should take care of that. But would that lead to more productivity, creativity and progress? Or would it hinder productivity, creativity and progress? The desire to mate/create is a powerful motivator for work and production. But it can also be a source of destruction and decay. Would we be better off like our pets - spayed and neutered and without any hope and urge for mating?