The evidence is weak, but currently leans towards "parents can and actually do a better job than the professionals." This includes parents with low incomes, and includes parents with low educational achievement.

You categorize this as contributing to segregation, but I say that it contributes to diversity. Public school is a hugely homogenizing force and the homogeneity it targets is not necessarily good. I think it is good for society to have a set of people who were raised in an environment with fundamentally different experiences and priorities.

https://www.psychologytoday.com/us/blog/parenting-translator... https://www.nheri.org/research-facts-on-homeschooling/