Can't touch roadkill around here. It's illegal possession, any way you look at it ("roadkill tags" don't exist).
On top of that, animal control can take as much as 9 hours to respond to a call; and Sheriff's deputies or Police officers are not allowed to discharge their weapons to dispatch non-threatening animals. So, anything that's injured gets to die a nasty death in 99% of the cases (very few people are willing to slit a throat - if they even have a knife available).
There's a stretch of road near me, that has about 1/2 mile of open space where it crosses a river, between two suburbs. In that 1/2 mile stretch, I figure there are 6 to 8 deer killed every week, on average. Very few of them die quickly, and most get left to rot for 5-10 days before animal control picks up the carcasses.
At the very most, they'll send a Sheriff's deputy or animal control officer to lop off a buck's antlers with a saw or bolt cutters, and drag the body farther off the road.