Erika - my kids go to public school homestudy programs that are very much like you've described. We're fortunate that the programs offer weekly optional workshops that my kids can take, have curriculum available in all subjects, which can use or not, and have almost total freedom to educate them in whatever way the family sees fit (I say almost, because technically, we have requirements - although they are very loosely defined). I even know several radical unschooling families in each of the programs my kids are enrolled in. So...I know that what you've described can work - because it is working in our community.
There is a caveat though, and it is also one of the reasons I voted *against* vouchers in California when the proposition came up years ago: When tax dollars are involved with education, the system requires "accountablity." What this means in my son's program at this time, is that they strongly advise the kids to take the standardized tests each year, because the program has more than 99 kids enrolled, so money for the program is tied to test numbers. My dd's program has fewer than 99 kids enrolled, so testing does not effect their income. My kids do not take the standardized tests, because I exercise my right to opt out. I told my son's consultant that I was opting out for her, and her colleagues' sake since I thought it was appalling that one high stakes test can be used to fire teachers. I have a big problem with the high stakes aspect of the tests. She understood, but still wished I'd let ds take the test.

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I think a voucher system would also effect private schools, and give them less freedom to educate the way they see fit, because when tax dollars are involved, the government wants accountability. Soon, the private schools would be required to give standardized tests, the tests would soon become "high stakes" and the private schools would begin teaching to the tests in much the same way the public schools are now doing. The other problem with vouchers was that the amount they were offering per student wouldn't even cover the cheapest parochial school's tuition. I thought it was a scheme devised by the wealthy who wanted some assistance with their children's private school tuition.
My son was actually going to an independent secular private school at the time, so presumably I could have benefited from vouchers directly, but I still voted against them.
The Belgium system as described on the program could be a better system than the voucher system, but I'd still be wary of "accountability" and it's effect on the way the schools could operate.