As for schools teaching kids about the common culture and all that, as a conservative I couldn't agree more. But is there evidence that public schools are better at it? The results of the 2006 National Assessment of Educational Progress history and civics exams showed that two-thirds of U.S. high school seniors couldn't identify the significance of a photo of a theater with a sign reading "Colored Entrance." And keep in mind, political correctness pretty much guarantees that Jim Crow and the civil rights movement are included in syllabi. Imagine how few kids can intelligently discuss Manifest Destiny or free silver.
Right now, there's a renewed debate about providing "universal" health insurance. For some liberals, this simply means replicating the public school model for health care. (Stop laughing.) But for others, this means mandating that everyone have health insurance - just as we mandate that all drivers have car insurance - and then throwing tax dollars at poorer folks to make sure no one falls through the cracks.
There's a consensus in America that every child should get an education, but as David Gelernter noted recently in the Weekly Standard, there's no such consensus that public schools need to do the educating.
Really, what would be so terrible about government mandating that every kid has to go to school, and providing subsidies and oversight when necessary, but then getting out of the way?
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.