Of course schooling outside the home does not change any of those admonitions to parents. Where do you get the idea that children so educated don't look to the parents for instruction? Mine always have. Or that parents abandon all influence over such children? How silly.
It takes only a cursory glance at the verses to know that you are distorting them tremendously as to their meaning. They are NOT social prescriptions but advice to parents regarding their PERSONAL interactions with their children. Proverbs and Psalms are my favorites in the Bible and I have read them many times.
There is nothing "rash" in pointing out that you are distorting the meaning of those verses. What is "rash" is the statement that Proverbs is applicable to education in the 21st century any more than it is to Nuclear Physics.