I've made a political case for appointing Hillary Clinton as Secretary of State--which assumes that fixing the economy, in the near term at least, takes priority over foreign policy synergy--but I should underscore a major practical drawback that would attend her appointment.
"An examination of how [post-WW II] national security teams functioned suggests some general conclusions about the do's-and-don't's of the appointments process. On the whole, decisions to appoint all-stars or worthies without significant previous personal connection to the candidates has, with the important exception of Kissinger, proved problematic. At best, they have been marginalized or ignored in the decision-making process ... at worst, they have caused significant disruption as a result of being seen as not team players."
Of course, you never know. Maybe Hillary is the next Henry Kissinger.