You mean a government agency will produce children? Why would the population vote for funding this if they don't want children themselves?
2. Most people actually want children. Getting someone to actually procreate with that will share burden.
3. Investing in children should hel to fund future pension payments. There is pretty good case for self-interest.
4. China won't care, neither will Russia or other parts of world.
5. Countries that will do that will have a better outcome than countries full of retirees. Unless AI takes over, natural selection will take care of rest