I wouldn't mind "competing" somewhat here, but the public schools get loaded up with more and more regulation while "alternative" schools with guv funds getting less and less every year.
Public education isn't "free" per se, but they have to take pretty much everyone as opposed to private schools who don't have to and can limit enrolment (and toher things too). I do want the private schools to keep those freedoms, not be intruded upon by government.
You make a good point, and some who favor private education have said that with a voucher-type program may come a trainload of new requirements attached to public money -- free condoms program, diversity training, etc. and so on. In the end, the loss of freedom may not be worth the infusion of public funds.