At zero times in human history when something was de-funded or de-regulated did the cost of it or alternate services go *down*.

If you take $5,000 out of a household's tax rolls for a voucher, the cost of the nearby private schools *will* climb $5,000 within a month or two.

And I don't know any private schools whose annual tuition is less than about $12,000. If a family already doesn't have a thousand+ bucks a month to spend on school, giving them three or four hundred isn't going to make up the difference.