The post I was replying to said that free parental leave would allow parents to "give their best to the economy" and reach their "full potential" at the career. To me that implied American work culture and "greedy jobs." (Google the term, there has been a lot of commentary on it).

From what I understand, most European countries optimize for something like "cozy economic conditions" rather than "maximizing economic potential" so neither my comment or the comment I was replying to would apply Europe. What I have seen in the U.S. is misery resulting from two parents working greedy jobs, like one is a high-powered lawyer, the other is engineer at a startup and then having a baby or 1 year old or two year old in daycare. One is a sales rep, the other is working a political campaign. What do you do when baby is sick and dad has to make sales quota and mom has a deadline for engineering documents that the entire construction project is bottlenecked on? What do you do when both parents need to stay late at the office, one to finish the legal docs big deal, the other to make a product launch deadline? Stress and fights over whose job is the most important results. What if baby is sick and waking up at night every 30 minutes? Who gets to be sleep deprived?

Then you get your kid to preschool which is either paid or free. In this way the mother (who usually has more burden related to breastfeeding etc.) can finally breathe freely. Can she go to work? Yes, and in some Europaen countries she has the right to ask for part work with the current employer, and they can't refuse. A few years later the kid goes to school (again, paid or free) and parents can decide how they organize their lives based on their needs an expectations. If your kid is sick, you can stay with them, and I always assumed this is normal and civilized way, I can't imagine otherwise.

I am curious though, would this job that mom goes back to actually be more "productive" than taking care of a four year-old and two-year old human child?

If that is what you mean then I seriously doubt your claim that there are few non-greedy jobs that contribute to the economy.

What I said is "that contribute to the economy enough to be of more value than childcare" Picking up trash or painting houses are important jobs that contribute to the economy, but they are not more valuable than caring for children nor do they pay more, so there is little point in a second parent going back to work as a house painter and then paying for daycare, or having the state subsidize daycare.

In a medium cost-of-living city in America, two kids in daycare will cost $40k-$45k. There aren't many non-greedy, non-sinecure/subsidized jobs that will pay enough after taxes and commute costs to make entering the workforce worth it. And I don't see the point in actively subsidizing the childcare versus giving all parents some assistance and then letting them choose the more economically efficient path.

I don't want to optimize for the economy... but if I did ...

Instead of having the second parents work the non-greedy job painting a house or what-not, and then third-parties working in the child care industry ... just have the second parent take care of their own children and the third-parties painting the houses or what not. Your equation leaves out that the parent taking care of their own kid frees up the workers from the daycare industry to do something else. So their is no net loss in output. It only is a net loss if daycare is so much more efficient at taking care of kids that one day-care worker can free up multiple parents to work non-greedy jobs, but when you look at the all-in costs of daycare including administration and facilities and floaters that is not really the case.