Harvard Law is heavily represented, but Harvard's Kennedy School of Government didn't get a token appointment. It's a rather sad state of affairs, if for no other reason then it aligns the incentives in favor of a longer, costlier, and less directly relevant education. And beyond that, it's a bit weird that so many folks go to law school in order to not practice law. Government is using law school as a credentialing process rather than an educational tool.
As Rodrik notes in his post "If you are bright and are contemplating a potential career in American politics, you go to a top law school--not a public policy school." Of course it's no secret that many politicians are attorneys, and there's nothing all that scandalous about that fact; after all, someone who's job it is to craft laws ought to have some training in understanding and interpreting them. But it's also true that a career as an attorney can prove a gateway to a public policy position in which the job of being an attorney hardly seems to be a qualification. As I learned in law school, it's not what you know, it's who you know. This is certainly more true in politics than in any other field, where politicians feel it necessary to select for certain jobs persons who have been vouched for by other people that they know (or vouched for by people who are known by people they know) largely out of a desir to ensure competency and loyalty.
Of course, we shouldn't presume that attorneys aren't competent to deal with the non-legal tasks they are assigned. No one would question that Hillary Clinton, a graduate of Yale, is unqualified to serve as Secretary of State by virtue of the fact that she lacks formal education in statecraft. Many attorneys who rise to these ranks have served in positions that anything but legal in nature, a number of them obtain Master's and PhDs in a non-legal field (Susan Rice, for example) and in truth, many people are attorneys whose interest and talents lie in the fields of politics, economics, statecraft, and so on.
So what does this mean for all those bright young students at public policy schools? I don't think they should be discouraged. For one, just because the heads of various cabinet-level positions are or were attorneys, doesn't meant there aren't thousands of positions available for those with a demonstrated commitment to public policy. The Kennedy School of Government alone has churned out quite a few prominent graduates. And should not be forgotten that while political appointees may direct the organization, it's civil servants who will turn that direction into practice and policy and who themselves can rise through the ranks.
Still, it would be interesting if someone would do a study of the graduates of public policy schools and see how their graduates fare (if there is one out there, I can't find it.) I tend to believe that as public policy schools grow more widespread and pre-eminent, more of their graduates will occupy roles in the federal government.