> hand-picked by parents to keep away problem children

Unless you can magically guarantee (or have enough money to fund their whole life) your children will never have to interact with "problem" people, they will need to learn to deal with those people one way or another. And it's better to do so in a low-stakes situation like school.

Childhood and youth are anything but “low‐stakes.” The social experiences I faced in public school were far worse than even the worst parts of my adult life. The direction I was headed was one of dark cynicism and misanthropy thanks to the bullying I faced and the lack of care from the adults in the system. When I switched to homeschooling, I began interacting with rational adults (my parents’ friends) and in turn learned what functioning human relationships look like. My ability to weather the difficult storms of adulthood in a healthy way came from the social growth I gained through homeschooling, not the regressive “socialization” that public school inflicted on me.