There is a theory - called the Big Tom Theory - that hunting pumas actually increases conflicts between people and pumas. If true, it might be reason enough to ban hunting. Here is the theory. In areas where pumas are not persecuted by people, it is a fact that the number one cause of mortality among young pumas (at least males) is being killed by a resident male puma. These resident males, or big toms (a tom is a male cat - as in the cartoon Tom & Jerry), are cats that have survived and established a territory because they are secretive enough to learn to avoid people. Hunters, however, usually go for a Big Tom as a prize. So when one is taken out, the inexperienced young males thrive and often get themselves into trouble with people. If the Big Toms were left in place and not hunted, they would take care of the young males that are not secretive enough (the kind that usually get curious and enter human areas) and only the really secretive shy ones would survive to adulthood.
Something to think about.
