Plenty of charter and private schools provide better education at the same class sizes and half the cost of public schools.
I think one component of that is that students whose families just want to dump them into a free day care wind up in public school, and families who are engaged in the student's education try to get them out of public school. These play a role in the educational outcomes, but there's still no good reason that the lesser option should cost so much more.
And as for the "poor teachers" spiel, save it. It got old decades ago. There aren't a lot of 4 year programs you can walk out of starting at 30k/year with full state benefits and working 9 months out of the year. A friend's sister just retired from public teaching making 6 figures, and now has a pension in the mid-80's. Yeah, when they work they do work hard, it's not an easy job (if they're any good at it - I'm sure it's a cake walk if you don't really care), but they aren't on food stamps.
It is much harder to find a job than to keep one.