Disagree. Everyone needs to realize that having two parents who both have "greedy jobs" is a path to misery. Giving out childcare does not change the situation. One parent will always need to step back from their career or there will be misery, I've seen too many cases. Even if both parents are comfortable putting their kid in daycare 9 to 11 hours a day (to cover both the workday and the commute), which they should not be, they still have to deal with many sick days, needing to be out of work by 6pm every day, not going on business trips, teacher's conferences, school plays, PTA meetings, not getting a good night sleep because baby or toddler is having a sleep regression, etc. etc. There is no world where you provide everyone universal childcare and now both parents can "work to their full potential" and "give the economy their best."
The reality furthermore is that there are few non-greedy jobs that are non-subsidized/non-fake and that contribute to the economy enough to be of more value than childcare. Subsidizing childcare, so the second parent can get a non-greedy job as a neighborbood coffeeshop owner, or working as a strict 9-5 government lawyer, isn't really a win for the economy.
If the economy is what you're trying to optimize for.
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.