Haven't you noticed that anytime the federal government disburses money to any person, organization or state, the federal government regulates that recipient? There are no end of court, including the Supreme Court, rulings that government financial involvement in anything gives the government the right to interfere.
It may have been originally your money, but once it gets to the government it becomes "public" money, and giving "public" money means regulatory agencies have the "duty" to insure it is spent "responsibly".
Therefore, if a voucher program is started it won't be long before the curriculum in any private school that accepts a student that is government funded must accept changes. You know, teach exactly what you go to a private school to avoid exposing your child to?