And why do you think those schools fail? It is a much larger system wide issue rather than the 'monopoly of the public school' as you state. I could literally dive in to a 5 page post about the issues but you said it yourself.
http://www.economist.com/blogs/democracyinamerica/2016/10/preparing-pass-baton And unless you can point to a school that literally graduates 0% of it's student base, then you can't say your public schools are failing 100% of the time.
So here is a very generic question that you can answer: Should the girl who is the first chair flute player...stands about 5'3 and weighs about 120 pounds...be expected to dunk a basketball just like the varsity starting center who is 6'8 and weights 220? If you said 'no,' then why did they and still attempt to judge students on ridiculous testing that proves nothing and standardized tests that are so generic and flawed, they are some what useless. BTW, I am not saying that all testing is bad and that SAT's and ACT's aren't useful. What I am saying is that if you want schools to improve, maybe give the power back to the classroom teacher and increase their salaries and wages and maybe you'll start to see students achieving at higher levels.
I am a damn good teacher and love what I do. Did I get in to it for the money? Nope, and most teachers will tell you the same thing. But poor pay and being dumped on sure doesn't help the recruitment of more teachers that may choose other lines of work instead. Want to see schools improve in the state of Indiana? Increase funding for our teacher salaries and continued education and watch more higher ability-college bound students WANT to become teachers and STAY teachers.
Like my father, who was a teacher, told me: 'Not everyone can go to college, and that is fine. We need people to pick up our trash and to lean bathrooms. We also need people who can weld, change oil, and provide other services that aren't likely to be taught in school.' Want to see a change in our school system in Indiana...create technical high schools where students can learn skills that they can adapt and use after their graduate high school because not everyone wants to go or be ready to go to college