There's no way they could do worse. Kids might get enough sleep, and learn about something relevant if parents were commonly able to keep their children from the grinders of the school system. They also can keep their attention on the kid unlike schools that are jammed to the gills with kids. Better food for sure.....And no bullying(a CDC listed main cause of suicides)
Home schooling allows for the ultimate in student centered learning and small class size, however in this society where often both parents work full time during the day, it is often impossible. When home schooling is possible, however, the parent is able to make sure the child fully learns and retains important information, which a teacher caring for 30 students at a time cannot do.
It is easy to denigrate teachers and schools, however these people are trained professionals with proven qualifications in their subjects. Some parents might be capable of home-schooling their children, but most are not. One can also question the reasons for home-schooling; our schools are underfunded, class sizes are huge, extra-curriculars are being cut, and so on. If people are so worried about a better education for their children, they should support public education with better resources.