Usually the offensive coordinator is in thepress box, which does give you a view of the whole field and ability to see offensive and defensive plays as they form.  It is a great place to call plays and/or communicate play calls to the Head Coach.
As a Head Coach, I would never leave the field to be up in the box.  I think it is very important to maintain eye contact with your players.  It gives you the ability to communicate the importance of the next series. 
I believe the Head Coach is not only the offensive strategist, but must be the person to instill vim & vigor to the player, to lead and inspire, and to coach each player as much as possible during the game.
The Head Coach belongs on the field.