I could be wrong but I think a lot of parents just simply turn that responsibility over to the CCD teachers.
You are right ... and that is where they are wrong. I speak from personal experience. Like so many others, I registered my child in a catholic church on the assumption that they would do the catechesis. they did ... but I should have done more at home. Now I encourage all parents to get involved and begin educating their children when they are young. The Baltimore Catechism is an excellent starting point.