An excellent way to destroy a country's productivity.
Listen, if you want the government to incentivize having children, then establish tax consequences. Same way as the government can force you to pay a tax penalty, the government could force people older than a certain age who are still childless to pay a "societal development" tax. The proceeds of the tax go towards paying for free childcare.
With regular police visits to ensure you're not secretly using this time to work, or get education, or self-improve, because that would be unfair. In fact, it would be more efficient to just put such people in a low-security prison. With video games and well-stocked mini-bar of course, after all they are not criminals!
Listen, if you want the government to incentivize having children, then establish tax consequences. Same way as the government can force you to pay a tax penalty, the government could force people older than a certain age who are still childless to pay a "societal development" tax. The proceeds of the tax go towards paying for free childcare.
/not sure if I'm serious about the above or not