"Would you rather go back to the time when only the children of the wealthy would be educated by private tutors and the children of the poor (who couldn't afford to have their children educated to even basic standards) went into work as soon as they were able?"

That is not entirely a thing of the past. My zoned high school in New York City only graduated about a third of its incoming students when I was a teenager (I was fortunate enough to go to a more well-funded school). What do you think those high school drop-outs were doing? Some were in gangs, others were out working. There are still families that are so poor that they start pressuring children to work as soon as the law allows it.

"Without school how do those kids get an education?"

A large number of those drop-outs are only barely literate, and only barely able to do basic arithmetic. The question is not, "How can they be educated without school?" but rather, "How can they be educated?" We still struggle with that issue.

"basic numeracy and literacy skills a child needs to function in society."

As it turns out, the minimum literacy skills needed to function in society are taught somewhere between 2nd and 4th grade. You do not really need to be able to read at a more advanced level for many lines of work, where your vocation training is entirely hands-on and where you have calculators or computers to do your arithmetic and logic. My mother is a blue-collar worker, and some of her coworkers are only barely literate enough to fill out incident reports (she often has to help them). You do not even need to be literate to vote in a national election.

The problem with being uneducated is not that you cannot live -- people with no income can still survive in our society. The problem is that an uneducated person is at a great disadvantage in our society, being cut off from opportunities and being easily taken advantage of by educated people. Uneducated people are far more likely to waste money on the lottery. Uneducated people are far more likely to forfeit their right to remain silent if they are arrested. Uneducated people are far less likely to attain leadership positions or financial security.

Unfortunately, the public education system as it exists today utterly fails to give people the minimum education needed to avoid all of the above. I suspect that giving people the education needed to be leaders or compete effectively in our capitalist system (or, heaven forbid, to change that system) is not even a goal of the education system. Vocational training is not a goal either -- trade schools are popular for a reason. If you were to ask me, I would tell you that the goal of our education system is to produce compliant workers who accept their place in a rigid social hierarchy. It is not just the "bad students" who are punished in school; students who master the material of a course and then stop bothering to show up are equally punished, even when their teachers are fully aware that they are bored. Low grades -- in the D or even F range -- are given for failing to do homework, regardless of the education value of that homework. Punishments are doled out for insubordination, regardless of what it was that the student was doing (e.g. a student who was smoking pot in a bathroom will be punished the same as a student who cut class to go to the computer lab and learn how to program).

Really, this is a problem of values. We do not value education. The people in power, who received a quality education that focused on teaching them how to think, have little interest in ensuring that poor people learn anything other than compliance. If the goal were to ensure that people are learning to think, we would not be using structured tests where the precise subjects to be covered are known in advance to evaluate academic progress (nor would we be pressuring teachers to deliver high scores on those exams).