Please don't even get me started on public education in United States. I would gladly allow 3 more USPS organizations to waste taxpayer's money if they get rid of public schools and adopt a school voucher system.
Please look for 'Stupid in America' show on YouTube and watch it. It will seriously change your opinion about public schools. Also, how many times have you heard people moving to certain district because they have better public schools? Have you ever heard anyone moving to certain district just because they have better grocery store?
I fail to comprehend why you think profit motive is a bad thing. Just like a private school has a profit motive, the customer (parents in case of private schools) have an incentive to get best value for their money and trust me, they will.