I use them in a draw station, like all road kill. 3 days in summer a large raccoon will rend out. Small coons will break down in about 3 hours to just the bones and a grease spot. You are looking at this wrong though, in nature puts them to use, as that is what maggots are for. Put in a draw station which is open and vultures will appear too. It is all recycling.
I would make the point in your mentioning hating to get rid of problem animals. The reason they are there is because they are displaced out of nature as there are too many coons already. If they are dumped off some place, that is just compounding the problem in giving it to someone else in their sweet corn patch, or the birds will have their nests destroyed. Around here, coons often kill young kittens. I am in a drainage off a lake, and I get lots of dumped off animals, as the lake is such a nice spot for people to feel moral about, but I am the one who ends up having to deal with the situation. No one would want a prison opened and inmates dumped into their town as there was room and it was such a nice place. It is the same with raccoons and other animals, not wanting new pressures on the food supply.
Yes, I agree its all recycling, and thats what I currently do. I take them to "The Boneyard." My question of what else I could do with them was merely a question of if there is a better use than simply throwing them on the pile.
As far as hating to get rid of problem animals, I didn't say that. I said I hate the thought of wasting them if they have a use. I do not a relocate, I do not dump them off at your house. I do not help people that ask me to catch and relocate. Just as you mention, relocation is pushing the problem to the next guy.