I would argue those things are usually tied together. The parents who are more committed are generally those who have the finances and time to be committed and thus are already in the better schools.

It's the main issue in the school I taught at. Parents didn't care and kids knew and it rubbed off. Until the kid failed, then it was the teachers fault. They see no value in education, very generally. Rural southern school. And until that's fixed, and the social issues at home (kids sleeping in cars, only 15% of our kids had both parents at home, etc) we can't truly make improvement. But nobody wants to tackle the social issues.