That's primarily why home schooled students do so well in higher education.
So why is our educational system so adamant about breaking up the family? That is, we want to rip the toddlers away from their parents and put them in preschool. In some local schools, the K-3 kids go to one building, the 4-6 to another, the 7-8th graders to a third, and the high schoolers to a fourth building. If families have even two children spaced a few years apart, it gets crazy for parents to attend very many functions at all of those different schools.
We tend to think that bigger is better, that bigger is more economical. But having taught in a K-12 school where all of the buildings shared the same parking lot, and there were only 350 kids K-12, I can tell you that there was a much better family atmosphere in that environment than in the schools I attended growing up, or have taught in elsewhere. Not only was the holiday program attended by the entire family, it was attended by the entire community. Parents didn't have to divide up the responsibilities of so many nights out because there was only one event for all of the kids. They went to events as families. They got to know their kids' teachers, because the kids would probably have that teacher more than once. Excellent teachers got the benefit of lots of affirmation, and the community worked to keep them there. Poor teachers left after a year, because the word got around about them. Educators had important stakes in how things were done, because their kids were also students in the school.
My gut feeling is that a K-12 school should have no more than 400 kids attending. Everyone can actually know the names of everyone in the building if that is the limit, and we'll know who their siblings and parents are as well.
If the main indicator of student success is family involvement, then we should not make it difficult for the family to be involved in the child's education. We should be thinking through school structure and activities with the family in mind.
I would like to propose that school districts offer both kinds of education, large buildings divided by age, and small neighborhood buildings, more like one-room school houses for K-8 or even K-12 kids. Some folks actually think that changing schools as a child grows is a way to get them ready to transition to high school. I don't know what's so special about high school that we need to 'transition' to it. I also don't know what moving to a new building has to do with education.
My experience says that smaller is better, and families are happier that way.