It doesn't make an equal society, it shifts the inequality outside of the family. It's not more productive to care for somebody else's kid than to care for you

It doesn't make an equal society, it shifts the inequality outside of the family. It's not more productive to care for somebody else's kid than to care for your own; most parents would argue it's less productive, because they're more attuned to their kids' needs. So you need a certain amount of labor devoted to childcare in any society, and this amount is dependent only on the number of children, not the amount of income or its distribution. Economy-wide, if a market chooses who works, the incentive is to choose the people who make the most money. The arbitrage here is that if you make over the median income, you can pay someone who makes less than the median income to take care of your kids, keep your high-paying job, and everyone comes out ahead. But if everyone makes the median income, then it'll cost just as much to pay someone to take care of your kids as you make, making it economically unprofitable. And this is exactly how it plays out in real life. High-income families get a nanny or au pair, who makes a small fraction of what the mother does, but generally does better than she could've in other equivalently-skilled jobs. Middle-income families like teachers end up spending as much on childcare as one spouse makes. Low-income mothers drop out of the workforce when they have a kid, unless they have family help for childcare.