Citing GDP growth is cute, but as nothing has been done to address the underlying drivers of price inflation, we can reasonably expect that socialized child care will become an economic necessity. Any potential benefits of productivity gains will continue to be eaten by those who are first to drink from the monetary spigot. While GDP and hours worked may increase, living standards may not.
Also “having the state raise your children” sounds dystopian until you realize the alternative was them not being taken care of in many cases. Handing a kid an iPad is not raising them.