I think that the air rifles have many uses in a SHTF. Small animal hunting is one. Another use that I think we overlook is that many people will not have the food to take care of there dogs and they will let them go wild. Many of these dogs will attack people after being wild so the air rifle maybe a good weapon to keep them away or stop them.
Another problem will be the over population of rodents that will happen because of all the dead animals, people and trash. The air rifle will be great for stopping rodents.