I'm not wise enough to know the answer to all questions. But I do wonder why people have some weird loyalty to 'public schools'. In my world, the goal of education is to make sure that children are educated.
If a student can get that education at a public school or charter school or private school... I personally have no issue with that.
But some people hold onto some notion of the 'public' in 'public' school and think it is better. Some common arguments and my counter arguments are below.
1. Public schools makes children play together.
This is perhaps the biggest farce in history. Throughout the world, and I've lived in 3 countries (South Africa, Canada, and the US a few years back). In every country, parents will literally move to a 'good' neighborhood to let their kids go to a 'good' school. I'm pretty sure you could make an equally compelling argument that public schools segregate people more by making entire families move to new neighborhoods. This happened in Detroit as the biggest example. But I'm in Canada now and its pretty much the same. Public schools are not diverse. People self-segregate based on neighborhood.
2. Public schools can ensure standards of education.
Maybe at one point they might have had a case. But with lowering standards, just passing kids to get rid of them... you can't really make this case anymore. Besides standardized tests tend to ensure some minimal level of standards.
3. Something to do with money.
Right now, the rich can just send their kid to a private school if they want. If the poor/middle class want to, they probably can't afford it. Vouchers or having the government pay for it would help equalize things a bit.
4. Something to do with 'for-profit' schools.
This one can be easily solved by making sure independent schools are non-profit.
Canada is actually a pretty interesting study as schools are under provincial control, so we can see different models.
Canada has school choice for BC and Alberta. I could be wrong, but I think BC requires schools to be non-profit and both require fully qualified teachers.
What's interesting of course is that you can't really make a compelling argument that charter/independent schools bring about all the bad stuff people talk about.
On all the social stuff, BC/Alberta are pretty much the same as Ontario or any other province.
Heck, even Sweden has school choice.
So what's the harm in giving people choice to go to another school? The evidence would indicate, at least in a country like Canada, that society doesn't crumble and it allows various forms of experimentation and maybe it makes things better... who knows.
Rather than asking charter schools to prove they are so much better than public schools, why not ask if public schools are so much better that it justifies the government monopoly/tax dollars used exclusively for it.
The default position should be freedom of choice, Freedom can of course be restricted for a variety of reasons. But right now, based on the evidence, I don't see a compelling case that would justify it.