Answer: Shoes hanging on a power line don’t get burned for the same reason that birds standing on a power line don’t get shocked: they don’t give electricity a path to the ground, so electricity stays in the line and does not go through them. But if the shoes were to touch a power line and a power pole at the same time, they would provide a path to the ground and would get blasted with electric current. It wouldn’t be pretty!
By the way, if you ever see someone throwing shoes up onto a line, tell them to stop! The shoes can damage the power line, or someone trying to get the shoes down could be seriously shocked or even killed.