When a bunch of citizens are standing there watching you shoot the animal, heart/lung shots aren't immediate kills and lead to people calling and complaining on you.
Our normal animal control officers all get their rabies vaccinations, since I only fill in as an OT assignment, I didn't get a vaccine. Having gone through this series of shots, I am now vaccinated though. They also are issued .22 rifles to lesson the blow back risk. Again, no real need for a normal patrol officer to have a .22 rifle, so I don't have one and my department is too strict about training and liability so I can't just borrow one from an animal control officer. Many will just catch pole the animal and blue juice them.
Ken, check and see what the cost is for the vaccine. From what I have heard, it is not cheap...