I think it's definitely valid to demand choice, and a public school system is remiss if it doesn't offer much.
For example, a city the size of Portland, where I live, should have ample public schooling on the same-sex model, meaning all girls or all boys -- not exclusively, but in addition to the "more normal" (by today's standards) coed kindergarten through high schools. Based on recent government reports, I'm thinking that's actually a likely prospect.
But that's not imaginative enough. We could have public system alternatives that are radically different from the norm, to make diversity even more real. For example, what gets taught in the vicinity of tribal sovereignties aka Indian Reservations? Why shouldn't that content be altered to include optional flatscreen based math from Python Nation? That'd be a new choice for deserving, patient Americans.
Plus other public schools could subscribe as well (given we're talking cyber-assets a lot of the time, meaning duplication costs are quasi zero, and Uncle Sam likes being thrifty when the economy allows it -- this appeals to fiscal conservatives especially).
I'd prefer to see radical diversity within the public system, offered to satisfy the legitimate demand for choice, than see taxes leaking away willy-nilly, to private schools which might not have the same level of commitment to keeping the USA active and healthy over the long haul. When citizens pay taxes, it's to make our nation great, not to aid and abet raiders and looters of its treasures.
Originally published to the Math Forum.