Sure ticks me off that you cant keep them.
Must be a state-to-state thing.
Here in Ohio you can keep them if you wish. Far as that goes, many LE agency's here in Ohio have lists of people they will call that have made arrangements saying they will come pick up deer killed in accidents if the vehicle owner doesn't want the deer.
LEO just writes you a form to make it legal. Saves the taxpayers $'s from having to have a gov't employee deal with the carcass.