I really shouldn't continue this because it's clear from your posts (and past discussions) that you're deeply steeped in the tea leaves and unreality of Ayn Rand and I'm certainly not going to change your mind, but in the spirit of discourse:
Without being able to cite SPECIFIC reports, I base my assertion of "better" schools in Sweden, Japan, and Germany on the basis of the frequent (yearly) reports which emerge in the media ranking the scores of students, from many countries, in a variety of academic subjects (geography, math, science, etc.). US students inevitably fare poorly when measured against students from other countries.
Your profit-motive proposition for schools is devoid of compassion and contradicts itself. Your "better" schools with the "higher tuition" spending "more money" on "better teachers" contradicts your assertion that all the "people with less money" have to do is get someone to start a "low cost/high efficiency" school. Well, if the "better teachers" cost more and, presumably, the "better schools" have "better" (read, more expensive facilities, materials, etc.), how the fuck can your magic entrepreneur offer the same quality? And if it were possible, why shouldn't the "better" (read wealthier) schools also operate schools on less capital outlay?
And please don't dribble vacuous cliches & euphemisms like "bang for their parent's buck" and "areas of economic unsweetness" into your discourse, it renders your ideas even less deserving of serious consideration.
Just curious but where do you go to school?