A couple of problems with that. Kansas is a rural state, and the overwhelming majority of the school districts are rural districts with no private school alternatives available. Second problem, do you know what kind of income a couple has to have to result in a $5000 state income tax bill? Depending on deductions it's well over $110,000. So again, when the state is facing a deficit why would you subsidize private school tuition?
Taxpayers NOW pay $10k/child in government schools.
Give that same parent $5k to use for a nongovernment school.
Savings to taxpayers: $5k/child.
Fixed costs complicate the issue, but the voucher can always be adjusted to result in a savings to taxpayers.
Regarding distance to schools, existing government schools could be sub-divided into government and nongovernmental schools. Schools could open in storefronts. Students could learn on-line.
Use your imagination. Yours are the arguments of the NEA.