If students and their parents have vouchers and a good attitude toward education, the rest will likely fall into place. If established schools didn't want to touch them, as you suggest, I expect new schools would start appearing to fill the gap. However, absent a desire to learn and work, vouchers may not help these kids very much.
That's the point I was making. There *are* private schools for kids who are in deep trouble, and who don't want to be in school, but they're very "special" schools. Here's an example of one in my city. Tuition is $16,000 a year.
Here is another program in my own city. The website doesn't say so, but most of the kids' fees are paid by the state anyway, because these kids are wards of the court. Most residential schools like this are *very* expensive.
I don't think that's what voucher proponents have in mind for dysfunctional high school students.