In Michigan, if you hit and kill a deer with your car you could contact the police department and get a permit to keep the animal. I'm not sure what it is like in other states.
Although I agree, and hate to see any animal go to waste, it is a little more complicated than it seems. My brother is a chef, and the laws and regulations regarding food care, handling, storage, and preparation of anything that will be served to the public are very strict. This may seem a little bureaucratic, but believe me that it is in the best interest of our health (just think of those kitchen nightmare stories you hear about). That being said, timely caring for the roadkill would be extremely important. As hunters we all know how important it is to field dress and cool the meat asap.
First you'd have to figure out who responds to the accident. Do you really want the police responding to a dead deer, or do you think they have more important issues to deal with? A game warden? I know in the two states I've lived in (Michigan and Oregon), they are spread so thin that the this isn't realistically possible to drive around their district to file reports on car/annimal accidents. Maybe there is some volunteer organization out there that could be designated to handle the meat, but I don't know of any state agency that would gut, butcher, store, and disperse this roadkill meat for free, so you have to ask yourself if you are willing to pay to make it happen....in the form of taxes? Unfortunately, in the end, there are probably cheaper alternatives to provide food to the homeless.
You might think that since there are homeless and hungry individuals who need the food, there are ways around some of the food handling guidelines that would get this meat from the road to their plate in a cheaper and quicker way. There are some obvious ethical issues with that argument, and don't be fooled for second that the first person who gets sick eating meat that was not cared for properly won't go looking for some money from the agency or location that provided it.
In the end, I think the answer to reducing the waste is just to let anyone get a permit to keep the animal. If the person involved in the accident does not want it, allow anyone else on a first come first served basis to claim the animal.