“Sweden is not alone in encouraging competition from independent schools. Parents in Holland and Denmark have a legal right to state funding if they prefer private education. In the Netherlands, about 70 per cent of pupils attend privately-run schools that are state funded. In Denmark, support from only 40 parents is needed to secure state funding for a private school, and about 14 per cent of pupils attend independent schools financed by a voucher worth 85 per cent of the per-pupil cost in the state sector.”–David Green, writing in the London Telegraph


The mere fact that Scandinavia does it does not automatically mean it’s a great idea; perhaps the numbers of Scandinavian parents who send kids abroad for education is more meaningful.
But the mere fact the kids, regardless of income, are not locked into gov’t schools is worth watching for its outcome. My bet is that the schools actually try to compete in terms of scholarship.
But the US does it too, or once did. It was part of the Veterans Act. The government paid for a veteran’s education, even at private schools, even at religiously-affiliated schools. No one thought it violated the constitution.