Vouchers are a TERRIBLE idea.
As soon as the government okayed loans and grants to students of unaccredited, private schools, these things popped up all over the place, and most of them are diploma mills that do not prepare their graduates for real jobs. Some of them spend more on recruiting and advertising than they do on instruction. Much of the instruction is online, where the students can simply fake having learned the material. All exams are open book exams. What the private schools really like is that student loans cannot be cancelled by bankruptcy, making them easy to sell to loan vultures who will harass the debtors until their last Social Security check.
Everest University and its parent, Corinthian Colleges, has recently gone out of business. Most of their students never got useful degerees in anything, but they all racked up huge piles of debt.
These fly by night colleges get away with it because they donate huge amounts to politicians.
If vouchers are issued for elementary and HS education, the same creeps will grab the voucher money and deliver crap, just as they did in higher education.
Homeschooling is okay for the few parents who are qualified to do it: give them a financial incentive and it will multiply the number of scams.