It would have been even better to enact a law which says that all public moneys allocated for education are to be divided equally across all eligible (i.e. in the district area) students and available to use for the school of their choice (public or private). This would benefit poor/disadvantaged students as well as ones from wealthy families.
The tax write-offs turned into vouchers could be added to the above.
As with most things in life, the devil is in the details.
Vouchers don't necessarily mean that private school will be more affordable. Schools consider what parents are willing to pay when setting tuition and fees, so if a sufficient number of parents are willing to pay $10k a year to send their kids to school and the state offers a $5k voucher, instead of making tuition more affordable the school may very well decide to just raise tuition by the same amount. If you're willing to pay $10k, and the state is going to give you an extra $5k to pay tuition then the school can just raise tuition to $15k.
In my state, "education freedom" means that the state will give parents a voucher for schools, but the money for the voucher is taken from the school district the child would have gone to if they were in public school -- so the school has less to educate those still in the public school system.
The real kicker is the schools that parents can use their voucher for: horse riding lessons, dance lessons, cooking lessons, martial arts, etc.
I know a lot of people are not fans of even the concept of public schools, but this doesn't save taxpayer money it just takes that money and gives it to families that are more fortunate, and, really, do we really want to make it even more difficult for the children of lower income families to receive an education?