No more public schools?

In the Los Angeles Times, conservative commentator Jonah Goldberg has this op-ed, in which he argues that "[g]overnment is inept at running schools.  It should subsidize education for needy students, then get out of the way."  (A few weeks ago, in The Weekly Standard, David Gelernter had pressed a similar argument.)  Putting aside the partisan barbs, is there any reason not to agree with him when he writes:

Milton Friedman noted long ago that the government is bad at providing services — that's why he wanted public schools to be called "government schools" — but that it's good at writing checks. So why not cut checks to people so they can send their kids to school?

What about the good public schools? Well, the reason good public schools are good has nothing to do with government's special expertise and everything to do with the fact that parents care enough to ensure their kids get a good education. That wouldn't change if the government got out of the school business. What would change is that fewer kids would get left behind.