"Why do police departments accept guns from widows, etc, instead of directing them to a pawnshop or gunstore, where the widow might receive something for it? It would even seem unethical to do otherwise.........."
I've been on the police side of this equation more than once, and I'm a 'gun person'. You would be surprised how many folks (often widows) will say "I just want to get rid of this safely, so no one is ever hurt by the gun'. An ethical officer is in a bit of a bind. He can recommend a pawn shop, but not really specify one. Not many older middle class folks know where the local pawn shop is. One can offer to buy the pistol at a fair price. Some states, like Maryland prohibit face to face sales. They need to run through an FFL or the State Police, but most folks wanting to get rid of a pistol for the reasons above aren't interested in a multi-step process. Many cops will take the least troublesome path and take the gun, do the paperwork and have it submitted to Evidence for disposition. Personally, I think an officer offering a fair price to the person is the best of all choices, but it needs to be permissible in that jurisdiction.