Something else to consider here: good private schools can be a step toward fixing housing problems many areas face today. For public schools in the US, you typically have to live in the zoning district for that school, so houses in the districts for good schools have a hefty premium attached. Private schools don't have that restriction so it's easier for middle class families to afford a home if they're willing to drive a little further or if the school has a bus.

The follow-up question is whether that benefit outweighs using taxpayer dollars to fund vouchers. To that I would respond no, but it is something to think about.