Believe it or not, in the uber-Liberal island next to Seattle where we used to live, the local cops would "dispatch" hit-by-driver deer with their sidearms. Always surprised me, but I agree with the practice.Either the person who struck it or someone going by would call it in. We would dispatch an officer or deputy. If the deer was still alive and in bad shape the officers actually shoot them in the head to put them out of their misery. There were times where they would take off into the woods, usually the officers were good about going in and looking around to make sure it wasn't just inside the woods suffering.
I'm not sure it works this way in other places because Maine does have its own ways of doing things sometimes. The other key that is crucial here is that a lot of the time it's not a hot humid environment so the meat I feel doesn't spoil as quick. When I lived in Georgia and saw a deceased deer on the side of the road it never crossed my mind to try to salvage the venison lol