Grades 9 through 12 were extraordinarily crucial. My teachers from that period literally altered my life, and while I don't remember specific lessons, save a few truly memorable ones, what I learned in school was definitely foundational to the scientific understanding I've build since.
You're right, parental desire to educate kids, and educate their kids better than they themselves are, is a key component to the success of any education system. As is society and politics valuing education and not dismissing it as "elite".
If education seems reserved for the elite, that's not cause to dismiss education as useless, it is to demand that such class based restrictions on education be eradicated.
And if you want to change the system, you have to go a route that Americans are just not comfortable with. Education should be free. 100% free. It is a fundamental right. Not a fucking production that you pay for, and get better versions of if your parents have more money.