As a K12 teacher, what you've written here is inaccurate. Please pump the brakes on the dogma and the culture wars talking points.
The public school system is deeply broken, but not for the reasons you've mentioned. Schools are breaking because society is broken. School is not a business where you get uniform input A and produce uniform output B. Every student is different, and increasingly students are coming to school traumatized by the conditions of poverty and want. 10 million children are currently food-insecure, a number that has increased dramatically since 2008. Homeownership and the middle class have been eviscerated. It's really hard to learn if you're hungry, if your parents are too busy working to care for you, if your home is permeated by financial anxiety at all times, if your neighborhood is violent.
All of these things come to school with children. All of these things require more time, patience, and technical skills as a professional educator. This translates to higher costs, and/or lower scores. It makes sense that education budgets have gone up while outcomes have fallen: the inputs are changing. Education does not work like the private sector. Period.
Some of the things you said are true, certainly. Unions are problematic, administrative grift and bloat is a real concern, etc. But the biggest challenge schools face comes from outside our walls: more social problems, and funding/resources failing to keep pace. We don't need shareholder returns siphoning even more resources from students.
The free market would not provide a better education. Charter schools currently pretend they're better than public schools by selecting the best students and pumping out impressive scores, while the public schools have a higher concentration of difficult students. The comparisons are lovely for investor presentations, but the community is worse off. Some charters are great, but the free market model is not a silver bullet for America's education problems. IMHO, you need a mix depending on the needs of each community.
But organizing our education system entirely around profit and a family's ability to pay is guaranteed to entrench power on the one hand, and squalor on the other. We already see it with the college admissions scandals. Rich kids will go to good schools, poor kids will go to schools where the profit margins are thinner, and therefore the quality of schools are lower. "Efficiency" is great for markets, but not everything works like a market. Schools are one of those things.
My district is about to open its first charter. Here's what will happen. The kids who can get the best test scores will flow to the new school. The student body at the public schools will decrease, so some percentage of teachers will be forced to go to the new school for lower pay. The public school's scores will decline because we have a higher concentration of difficult students. The charter will use the juxtaposition to market itself and further erode the public school, even though the quality of education isn't actually better. Teacher burnout will increase at both schools (low pay at the charter, tougher jobs at the public), so professional quality and consistency will plummet. It will be harder to convince talented young adults to get into the profession, too, because of lower average pay. And the students lose every step of the way.