Voucher proponents want to get parents hooked on the idea of charter schools, and then the schools will invariably raise their prices past the cost of voucher when the undesirables start trickling onto their campuses.
There is a world of difference between means-tested vouchers and non-means-tested vouchers. Non-means-tested vouchers will have the effect of making expensive private schools more affordable for the upper-middle-class, while means-tested vouchers can't do that.