Not just any human soul, just the magic users, which explains why they have to be here. The cat and the dog, due to not being able to sent the souls to limbo directly, might just have to fight for their side like normal for the iguana to eat.

Maybe a school nurse can use magic to repair all damage to the bodies and keep them somewhere to remove the previously mentioned plot hole. She got both sides to agree to let her clean up after the battles along with the school maids.