Seem to remember something about Sun Tzu saying to only surround an enemy on 3 sides...
“Sun Tzu’s The Art of War strongly emphasizes the use of flanking, although it does not advocate completely surrounding the enemy force as this may induce it to fight with greater ferocity if it cannot escape.[3]”
http://en.wikipedia.org/wiki/Flanking_maneuver
With respect, we are not trying to politically demoralize this enemy. We ARE trying to destroy them, and a fully surrounding maneuver, no matter how hard it makes them fight, allows each last one to be killed without the possibility of living to fight another day.