Single Payer vs Single Provider

Megan McArdle poses the question of the day.

should one be required to stake out a consistent policy across school and healthcare funding? Or can some single-payer supporter explain to me why healthcare will work with what is basically a voucher system, but education won't?

To which Kevin Drum replies:

My initial answer is no, there's no reason to be consistent here. Healthcare has some unique characteristics that (I believe) end up pointing toward single-payer as the best, most efficient solution for universal coverage.

Drum goes on to say he favors the status quo in schooling: a combination of public schools and charter schools which are not funded or subsidized by the government. Basically what he favors is a single-provider system with some private education available for those who can afford it. I'm not sure that answers Megan's question to anyone's satisfaction. And I certainly don't feel that the best way to improve education in inner cities is to leave things the way they are.

Here is my attempt to answer Megan. I favor a single-payer healthcare system because there is a great amount of risk involved in health. The current system of pooling risk through employer based insurance is inefficient and becoming more so as employees become less attached to a single employer.

Education is less about risk than about providing a public good: educated citizens.

Update: Matt responds with a good point about the non-feasibility of a national single-player education system given our starting point. If we can agree that such a system is a good goal why are vouchers considered such a bad step toward that goal?