As a libertarian Falangist, I'm leery of the notion that primary and secondary education should be handled at any level other than the most local, partially because schools do serve as a focus for community and partially because I think the Feds do a poor enough job with all this New Deal/Great Society crap that they need to get back to their core competencies and work on getting those straight for a while.
Unfortunately I can see what Cobb and Hirsch are saying, and I find it hard to disagree that "...a shared national cultural core is vital to the strength of our democracy." This is a nation built on law and respect for law that creates order, and we are well on our way down the road to a sort of feudal socialism where the Anointed Ones will prescribe for us what is right and correct so that we can follow that prescription and dumbly give up our tax dollars to pay for it. The next thing you know we'll be as screwed up as the Brits. I don't see any other way to break the iron triangle of administrators, unionized teachers, and other people who are doing just fine within the existing system unless we bring the heavy hammer of the Feds down on all these local systems; perhaps the states can do this, but it doesn't address the cultural problem that Cobb and Hirsch are talking about. The only way to really win the culture war will be to retake the schools from the Left, and teach the children what they need to learn to be productive, involved members of society instead of criminals and leeches. It can be done. It must be done. The only question is how it's going to get done.