How the hell can a school be "private", while being funded by taxpayers?
There is nothing wrong with firms making profits, it is a sign of efficiency, and a sign of where resources should be allocated; with time, the least efficient firms are eliminated, and only those which create the most value at the lowest cost remain. The problem is that the product (and its value) may not reflect the objective(s) of the policymakers and the public, and the chief goal of those creating any system should be to properly align rewards with desired outcomes.
There is another solution. You could set up the markets so that the way to maximize profits is to create the best solution. For example, imagine if we had a perfect measure of student outcome. You could make the school's pay dependent on their outcome, then the market will find a way to maximize the f(outcome)/cost.
The obvious solution: more tests, and more bureaucracy. By the time you've got enough tests you might as well have a state-run school.
I would argue not, or at least that externalized costs need to be internalized somehow (regulation or taxation are the typical means).
That is to say, if we have for profit public schools, I'd want their profits to be tied to the long term effects of results of their students, not to yearly test scores.
This is a great idea! Why not do the same for government-run schoolteachers? This may help attract and retain high quality staff, as well as providing low-skilled teachers an incentive to leave.
The system is a disaster, with a lot of for profit schools slashing costs to maximize profits regardless of what the consequences are for the students. And that's just one of the many failures of the system.
Basically, the problem is that markets don't necessarily generate the best solutions from a social perspective, markets generate the solutions that create the largest profits. You have to some how get the markets to stop chasing profits, which is easier said than done.