The solution is to do what Sweden does, which is to require all schools to accept the vouchers and charge no further tuition.

The bare bones the market would create would depend on if people really want K-12 to be a glorified daycare or a useful tool for imparting knowledge. But having a financial incentive to function or go bust would mean you'd at least get better daycare services.

I would say yes. Most states schools provide excellent value, and I would even extend that to community colleges which provides even better value for their students.