Probably only necessary if you want to avoid property tax issues and legal recourse; like all the other parents who homeschool or send their kids to private schools. Those people aren't given a tax break or reimbursement. Any property owner has to pay school taxes even if they have no kids in the public school system. I don't have a problem with restoring money to the parent who homeschools or private schools but many people do. The reason for that is that somewhat twisted reasoning that if you get a tax break, that is equivalent to receiving subsidies from the government. The "logic" (and I use the term loosely) is that a tax break is the same as receiving money. That then makes you subject to federal regulations governing government supported schools. Then some people will try to use that as a wedge to then be able to control what you're teaching.
What you're proposing sounds suspiciously like the voucher system. Go for it.
In our state, education is, as you say, covered primarily by property taxes.
Interestingly, as a pastor, I can opt out of social security and never have to pay a dime into it if I were to consider it in conflict with some belief that I have.
If that were treated the same as parents who choose religious, private, or homeschooling, then many would say that the government is giving ME a check for the amount that I don't have to send them.
Odd, isn't it?