Sure, but if you are a private school charging $20k a year now, why wouldn't you charge $25k when every potential student gets a $5k voucher? Then we need to increase the size of the voucher to meet the original goals of the program. Rinse. Repeat.
Every child must either meet some government-mandated educational standard, or enroll in a program which brings some threshold percentage of its students to said standard. $VOUCHER_AMOUNT is adjusted on a per-region basis based on the average tuition within each region. If the institution's tuition is higher than $VOUCHER_AMOUNT, the parents pay the difference out of pocket. If the tuition is less than $VOUCHER_AMOUNT, the parents keep the difference.
Parents obviously want to minimize the amount they're paying out of pocket, and they'd like to keep some of the voucher money, so high-end schools as well as low-end schools are incentivized to keep their costs down.
Parents putting their kids in K-12 private school aren't optimizing for cost. They are optimizing for exclusivity and educational "quality". If their school just became more affordable to the unwashed masses, they will gladly pay the premium to keep them out.
That is true for some subset of wealthy parents, and if they want to pay extra for exclusivity, that's their choice. But I think it's reasonable to assume that the parents of the 90% of K-12 students who attend public or charter schools [1] are prioritizing cost over exclusivity.
It's true that many families will pay more to buy a house in a good school district, but I suspect that the school itself isn't the whole story: rather, many people interpret the school district's reputation as a proxy for the safety of the neighborhood and socio-economic status of its residents, as well as a proxy for their own socio-economic status.
Ulimately, I suspect that with the free market voucher system I described in my parent comment, legacy private schools would continue to charge outrageous tuition. But I think we'd also see some new, possibly virtual "bang for your buck" schools which would compete on price and which would be exclusive due to entrance exams and high academic expectations for enrolled students.
I'm not sure I follow. Many students/families choose community college for the freshman and sophomore years to minimize cost. Many opt for state universities over out-of-state/private universities for the same reason.
Well, you see, we take the naïve dupes who borrow hundreds of thousands of dollars in non-dischargeable, uncapped student loans for an MFA in film at Columbia, and extrapolate that to the rest of the population.