I respectfully disagree. Plenty of people have no compassion for other people and would happily kill them given the chance, often the reason they don't is because they KNOW they will be hunted down and punished.
Would that concept apply to other crimes? Would anyone suggest that "laws won't work" when it comes to baby rapists? Or cop killers? Or child pornographers?
Should we stop imprisoning people that engage in those activities? Prison doesn't fix their lack of compassion, but it does limit the number of people that will engage in those crimes.
Severe punishment DOES deter crime. Right now many crimes against animals aren't punished at all, they aren't even THOUGHT of as crimes since the people without empathy think the abuse is normal.