It's been done. Some latin American countries have been the testing ground of these market based/privatized schemes. Look here:
Rethinking Schools Online
The most interesting comparison is from Chile, which has a long-standing voucher plan where pupils have been assessed regularly. The Chilean plan began in 1980 under the Pinochet military government as part of an overall "de-governmentalization" free-market package. It meets almost all the conditions of those in the United States who advocate "choice with equity," including fully subsidized, deregulated private schools competing head-on for pupils with deregulated municipality-run public schools in all metropolitan neighborhoods, from middle-class suburbs to low-income barrios.
One key feature of the Chilean plan was privatizing teacher contracts and eliminating the teachers' union as a bargaining unit. Teachers were transferred from the public employee system to the private sector. By 1983, even public schools, meaning those schools run by municipalities, could hire and fire teachers without regard to tenure or a union contract, just like any un-unionized private company. Another feature was to release all schools from the previously strictly-defined structure of the national curriculum and from national standards.
What were the results of this reform? The first was that even when parents' contributions are included, total spending on education fell quite sharply after increasing in the early 1980s when the central government was paying thousands of teachers severance pay as part of privatizing their contracts. In 1985, the federal contribution was 80% of total educational spending, and total spending was 5.3% of Gross National Product (GNP). Five years later, the federal portion was 68% of the total, and the total had fallen to 3.7% of GNP. Private spending rose, but not quickly enough to offset the drop in real federal contributions. Most of the decrease in federal subsidies to education came at the secondary and university levels, where per student public spending dropped drastically.
The second result was that in Chile, as in Europe, those who took advantage of the subsidized private schools were predominantly middle- and higher-income families.