You say this, but what you actually mean is no wealthy parent should be stuck without options.
The hoi polloi that can't afford the voucher plus mountain of money private school tuition will still be quite stuck without options, except that you've also created an explicit two-class system.
I hear those do wonders for social cohesion. As will opening a firehose of money into the insane fundamentalist indoctrination that so many parents wish to inflict on their children, but can't in public school.