What prevents the use of an EMAS along the sides of a runway?
I can think of a couple reasons why you might not want to expand EMAS all around the edges of the runway.  One is simply cost vs benefit:  If it is more likely that an airplane will run off the end of the runway than the edges it would make more sense to put the material there.  

EMAS would seem most beneficial in stopping forward speed if the wheels were to make contact uniformly.  An aircraft departing the side of the runway already has directional control problems.  The situation would be amplified if the wheel on the side “pulling” the aircraft off the edge was to be dramatically decelerated.  It could even cause a ground loop.