Sadly, this is not always the case with most children who go to public school. Parents have reliquinshed their parental roles, given them over to what they think is a higher authority, and stopped keeping watch. I also think parents like yourself are doing just as good a job as homeschoolers if not better in some cases.
The advantage of being in a good public high school is that there are advanced courses available that most parents couldn't teach, even with good pedagogic materials available. My kids couldn't learn Physics or Calculus correctly from me no matter HOW hard I tried.......and I'm a teacher (though I know there are some systems that have more than one parent teach in areas where they are strong).
When we realized how solid (and moral) our public schools were, we never considered homeschooling OR private schools......and we have seen the rewards of that decision many times over.