You are right because the government thinks of vouchers as THEIR money that they are distributing. And they think that the state has plenary authority over education. A proper education is what they say it is. The most neutral form of voucher would be to let families apply their school taxes to the school of their choice rather than receive it from the government. I ,for instance, could give my school tax to be used for the tuition of my grandson. But the educational establishment would die raher than allow this.
“But the educational establishment would die”
And the down side of that is....?
By Jove, I think you've found the solution! :)