Another reason safety helmet makers insist helmets should not be reused after an accident is that the energy absorbing component, which looks like styrofoam, is intended to compress and distribute force over a large area. The outer shell may look fine but the "foam" may have done it's job and is now less effective at absorbing energy. I've also known that material to become harder with age after picking up a motorcycle helmet I had laying around for years.
If the foam liner has become harder, more force is going to be transmitted to your noggin. noggin. (That last one was a joke)