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.
There are many public services we already rely on and there are many countries that offer free child care already in some form. What you call (forced) liberation is just societal specialization and not bad per se.
Focusing on fiscal/wage issues is a big and important topic though. I bet over time, budget hawks will reduce this public service like others and like in many other countries too. We are so many humans on our plentyful earth, we could achieve many things, yet, "we" lack money.