I wouldn't do it as vouchers but as charter schools and public school choice.  Rather than giving people a voucher, parents could "shop" for the school that they want their kids to attend.  There could be specialized schools - trade schools, language academies, math and science academies, art academies.  Some schools like an art academy or a special math school, the kids might need a test to get into but others would just be done by lottery.  This is how New Orleans does its school system.  There are legit criticisms of charter schools like them expelling problem kids and relying too much on standardized tests but these can be fixed.  There can be laws to prevent charter schools from expelling kids to up their academics and evaluation can be on other measures than testing (i.e. drop out rates, teacher evaluations, student engagement, graduation and college acceptance.)