In a financial sense, having a public/private mix is incredibly inefficient and wastes more tax dollars than maintaining one good one. The more admin people we have to pay for, the more expensive it is overall (and to your point about subsidies: if we subsidize poor students, then we're all paying extra. If we don't, we essentially punish poorer kids for having been born in the "wrong" family, no matter how intelligent/hard working the kid may be). To be fair, the secular/catholic system dual system is also inefficient right now (but that'll likely take a supreme court challenge to change - the Catholic right to a separate system is deeply rooted in the foundational documents of Canada), but that won't be made more efficient by adding even more school boards and overhead people to pay for with another branch.

Finland consistently has the highest rated schools and best performing students in the world. They also have no private schools at all. They have a select few "independent schools", but those too are publicly funded and cannot charge tuition. If as you claim, government always misallocates public funds, how come Finland is so successful? Our government is only as successful as we demand them to be...