It came up, sort of, in one of the threads about Catholic school funding in Ontario, but I thought it deserved a thread of its own. It seems to be a more-or-less accepted principle that we should have a ban on private delivery of health care services covered by the public system, so the richest people can't have a parallel system, poaching the best doctors from the rest of us, unless those doctors are willing to give up access to the public system altogether. It seems to me this principle holds even truer for education.
Where I grew up, in Tennessee, the public school system was mainly for those who couldn't afford to send their children to private school -- overwhelmingly poor and/or minority students (and those students who got expelled from their private school after being caught smoking weed in the bathroom). Teacher pay was and is abysmal, the school system was subject to a federal consent decree due to effective segregation, and the school I attended is likely soon to be shut down altogether under No Child Left Behind, leaving black students to be bussed across town or drop out of school altogether. In fact, the city of Knoxville shut down its school system altogether, leaving the encompassing county to pick it up, because the wealthier area residents largely had moved outside of the city limits to avoid paying city taxes, depriving the city of adequate funding for schools. On the teacher side, a teacher at Knox County public schools would likely need food stamps to feed two children. This state of affairs is allowed to persist because, as I said, the wealthy and even the middle class simply don't participate in the public school system.
I know that Canada's public schools are not in quite as dire a financial state as those of the Southern United States, but I also know they're far from without problems. It seems to me that if the wealthy knew their children attended public school, the pressure on the government to improve the quality of public education would be turned up quite a bit. A full-fledged ban on private schooling likely wouldn't fly in the United States for constitutional reasons (though I think it would still be worth giving it a shot), but in Canada, we have the benefit of Section 33.
(For the record, I think we should ban homeschooling, as well.)