The Washington Post has a long article by Emma Brown and Mandy McClaren on how Indiana’s school voucher program has fared (with Tom Pence), link here. The article posits what may happen under Trump.
Even well-off parents get voucher subsidy support to send kids to private schools. But an ethical question will be whether schools that discriminate against specific populations based on religious convictions should get federal subsidies, indirectly through parents. Some parochial schools, for example, will fire openly gay teachers.
The article says that some students indeed do much better in private schools. But in March 2016, the Cato Institute had held a forum which had shown mixed results in student performance, because of regulation, link to the forum video here.
Even the libertarian model encourages support of non-government instruments closely connected to families (parents) and faith models to impose their own standards of "belonging" on students.
FEE has some articles on the issue, such as "the failure of public schooling" here and the relationship between culture and poverty, here.
Some non-parochial private schools also do a very good job or producing outstanding students (for example, Potomac in northern Virginia), and a voucher program could extend the opportunity to low income families.