The difference is that dogs are BVR (beyond visual range) tools, and tasers, guns, batons are not. They are often employed where the officer can not see and control the animal and the officer is unclear of what is actually going on inside the building etc.
You are supporting the key point which is that dogs are not “cops” and killing them is not the same as killing an LEO.
Jackson wasn’t shot because he shot the dog, he shot at the officers. Aulf gave his life for his fellow officers, by deflecting the shooter’s attention and aim to himself.
One of the main purposes of a police dog is to reduce injury or loss of human life by sacrificing their own. This is why they are accorded officer status. They earn it.