Private school tuition is what? Private schools have to take any student that enrolls or can they pick and choose who attends meaning they are not forced to accept and teach those that disrupt classes for all others and supply special ed, beyond a certain level
http://www2.ed.gov/admins/lead/speced/privateschools/idea.pdf
If the USPS could charge a value for carrying all the junk mail it does that covered its costs, it might be solvent if not much closer to it.
While it would be nice to have every child attend a private school, the problem with that is that the cost would be no less and efficieny no more when private schools would be forced to deal with what public schools must. Private schools are like owning a business where you get to pick and choose your customers from a list of those applying to make a purchase from you. If they look like they are going to be problematic, if in no other way than to be disruptive of the other customers, one can regret to inform them that they are not an acceptable applicant. That amongst other differences are not often considered or mentioned in the rush to talk about how terrible public schools are versus private schools.
Public schools don't have the same luxury of exclusion that private schools do.
If private schools were economically less expensive overall, who would support a public school system?
While I agree that simply throwing money at problems does not solve the problem unless the money spent is spent in productive ways. It goes back the same old question of debt and investment versus dead ended "investment" or waste of money. Someone can borrow a sum of money they will use to invest in tools and equipment they then use to make money with and pay off what they borrowed at the same time. Someone can borrow the same sum of money and buy beer with it and literally piss it away.
I think people have to realize that public schools, by virtue of their being public, are obligated to serve all the public and based on that run into unavoidable expenses and inefficiencies that private schools do not run into and can exclude, by virtue of their being private. I think solutions can be found through innovation, but innovation requires an investment in more, not less, money, the point being the return on the investment will be many fold the initial investment.