Without changes at the White House, including the departure of both Susan Rice and Ben Rhodes, how is any Secretary of Defense meant to solve the problems that Hagel, according to the White House, was failing at? Defeat the Islamic State in Iraq and degrade them in Syria—but with no resources. Prevent the Afghan government from falling to the Taliban—but with no resources. Signal a strong front to the Russians in Eastern Europe—but with no credible threat of force or even serious diplomatic cooperation in the form of tough sanctions.
The task of the next Secretary of Defense is not enviable. This man or woman must be prepared to implement a series of overseas military campaigns that are not designed to succeed, but rather to satisfy domestic political considerations that the president be seen to be doing something about the Islamic State, the Taliban, etc. To do so while continuing to manage the hollowing out of the force through budget cuts and the implementation of social policies that are unpopular within the military. To be prepared to be micromanaged by a White House national security shop famous for its incompetence and raw politicization. To do so while maintaining total loyalty to the president and his incompetent, micromanaging aides.
There are plenty of hacks who could do this job, but they don’t have the credentials. And as for those who have the credentials: Who would want the job?