Charlie , if you waited strictly for the police to drop off road kills to feed your family you'd have to watch your kids cry in hunger. Especially in desolate places like northern Wisconsin.
First , you'll only get a roadkill if someone reports it and declines the deer , if it's not hamburger already. The police wont just see a deer on the side of the road and pick it up without knowing the time of death. The majority of time the person who reports it will claim it for themselves or someone they know.