Reward?  Carson serving as HUD Secretary would be a sacrifice - to shoulder the burden of public service.  He does not have to burnish his credentials.   There is more of risk and sacrifice to this than reward.  You yourself implied Carson s not not an egomaniac.  Is that a necessity for public service? 

I tell you,  it's hard to find men whose heart is in the right place.   Carson remains the most respected presidential candidate of this year's election.  I  think that is possibly all the qualification he needs.

As an alternative,  do you want to proffer a more qualified candidate?  You seem too quick at disqualifying this one.