Nathan, 

Weak analogy. You are sufficiently qualified to head John Hopkins University.  Why not?  Janet Napolitano is the president of the President of the University of California. She is a lawyer. (although she is unlikely to stop the malignant spread of the madness, 'political correctness')

There are many departments within HUD neither you nor Carson are qualified to head.  But as to the institution itself, why not?  At least Carson says he wants to end political correctness.  HUD is an agency that would greatly benefit from his prescribed therapy of political incorrectness with forethought & goodwill.  

I like Carson's personal example of escaping the nihilistic maelstrom of public paternalism that characterizes the urban poor whom HUD supposedly serves.  Maybe being a congressman first would leave him less qualified to clean up the malignant spread of bureaucracy.  Many get elected with good intentions but find themselves co-opted by the system they seek to change.  Why not?