I’d much rather see a tuition tax credit. Send your child to whatever school you want. If you pay tuition you get the credit.
To limit church/state constitutional challenges, the credit should be for whatever amount a taxpayer would have paid in taxes to support their own child's education had they used the state's education system.
This way a taxpayer would simply be redirecting their own education dollars to a school of their choice without redirecting the dollars of other taxpayers. This makes it difficult for opponents to argue that the state is paying for a religious education.
Call it "citizen directed education funding".
I'd generalize and go further by giving similar tax credits for things like home security systems.