Questioning your premise
Please explain how they are better. I'm not going to take that fact on faith.
The reason I say privatization would be a better choice than even the "better" schools in Sweden, Germany and Japan is that they could take advantage of the profit-motive (an idea that has been all but destroyed lately).
Profit motive in school-systems would mean that the "better" high schools (schools that put smarter kids into better universities and/or produce more productive alumni) would have a higher tuition, which means they'd have more money to spend on the better teachers, which means the students would be getting more bang for their parents' buck.
And for people with less money: it would be economically advantageous for the right entrepreneur with an affinity for pedagogy to start low cost/high efficiency schooling systems in areas of economic unsweetness.