Indeed, but if you send your kids to private school (or your social peer group does), then you have a counter incentive against supporting the public schools with your tax money and your political empowerment.
This happens with daycare (which is mostly private) and higher education (with private universities having a massive presence), and the society has yet to collapse.
The idea that it's perfectly fine to go to a a private institution years 0-6 and years 18-22+, but the 6-18 range is categorically and unequivocally better served by public institutions has not really been proven beyond reasonable doubt.
I don't think that I made any such claims. But to note a difference between those age groups, 6-18 is the only one for which we've declared a right to access for everybody at the present time. (At the very least, it's in the constitution of some states). The only way I can think of to ensure available capacity is to provide a public option. So I'm interested in how the public schools are managed.
I agree access is important, and it's interesting to see public school unions fight against charter, magnet and private schools in order to restrict that access.
With that said, notice how the distribution of private schools per capita drops significantly in highly-rated public school districts. There's simply no demand for them.
The private-vs-public battle only plays out in low-rated school districts, with one party holding the distinct advantage of being un-fireable.
I'm not sure how this is related to my comment. With that said, I suspect that religion dwarfs any other factor driving the demand for private schools.
In my state, the union definitely does not oppose private schools, and the magnet high school in my district is a union shop. The union opposes the state's growing voucher school program, but proponents of vouchers talk in "access" terms while promoting a barely concealed sectarian agenda. So once again, religion is a driving factor. Meanwhile, the union has been barred from collective bargaining on "working conditions" that include things like tenure. So, the ways that public school teachers can be fired, is at the mercy of the state legislature right now.
So far the voucher schools have under-performed public schools in the same districts, despite being given advantages such as more latitude in hiring and firing, and the ability to reject handicapped kids.