What prevents the use of an EMAS along the sides of a runway? The NTSB report about the crash of American Airlines Flight 1420 discusses whether an EMAS would have mitigated the severity of the accident, but concludes, based on testimony from a representative of an EMAS manufacturer, that


  ...the benefit of an EMAS in this accident would have been limited by the airplane traveling partly outside the runway edges; thus, the airplane would not have been able to use the full length of the EMAS. The report also concluded that an EMAS would have reduced the speed of the airplane by 15 knots but would not have enabled the airplane to stop within runway 4R’s runway safety area.  [report page 64/PDF page 78]


What I’m not seeing is any reason why an EMAS would have to be confined to the extended track of the runway; extending it from the ends up along the sides of the runway would provide additional protection for aircraft sliding off, or partly off, the sides of the runway (such as AA1420):





(Aircraft tracks shown in these images are merely examples of possible runway-excursion trajectories, and are not intended to represent any specific flights in particular.)

Am I missing something here?
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.