Your sources are flawed. The public school system was not started by industrialists to train the labor class. Where did you read that? It sounds like something from some Marxist pamphlet.
Marxist? ok... My understanding is that in the early 1900s industrialists like John D. Rockefeller and Andrew Carnegie dumped incredible amounts of money into legislation that established universal compulsory schooling.
Consider this quote from John D. Rockefeller's in first mission statement of the General Board of Education, “In our dreams, people yield themselves with perfect docility to our molding hands… We shall not try to make these people or any of their children into men of learning or philosophers, or men of science. We have not to raise up from them authors, educators, poets or men of letters, great artists, painters, musicians, nor lawyers, doctors, statesmen, politicians, creatures of whom we have ample supply. The task is simple. We will organize children and teach them in a perfect way the things their fathers and mothers are doing in an imperfect way". In other words, and obedient labor class.
He had many complaints, but being forced by the system to indoctrinate the kids was not one of them.
I'm suggesting that indoctrination is practically invisible at this point. It's systemic. It's built into the bells, and the sports, and the tests, and the discipline... and more so than when we were in school, the security. Tell me, did your teacher friend require fully volitional beings to raise their hands and ask permission to use the restroom?
I have no problem teaching kids stuff they don't want to learn. My kid is going to learn to read, write and do math, as well as learn history and science whether he wants to or not.
That's your call. But I would never attempt to force you to teach your kids things you didn't want them to learn, or thought they wouldn't need later. Basic reading and math skills I think are taught before a child is a fully volitional being. But trigonometry... not so much. I also don't think it's urgent for society to make sure that high school kids learn all these general subjects at the expense of what they have passion for. I seriously doubt Picasso would have gone as far in such a system. He was already making a name for himself at 16.
Then what do you believe is the solution?
Frankly I don't know. The question contains the premise that there is only one solution, which I don't accept. What I'd like to see is a greater variety of education strategies so that success could be observable and pursued by parents making decisions for their family. I think our current system is suffering from all the negative characteristics of a monopoly (increased cost, decreased quality and no incentive for customer service) and would benefit greatly from more competition.