Its probably not as easy to pass this dog off onto someone else as you might imagine. It makes little sense for someone to adopt a dog with a history of bad, aggressive behavior, and then pay to have a skilled dog trainer to (if you're lucky), make him behave, when you can just get a brand new puppy and train him right from the get-go with your family. Its really a long shot that Cricket's adoption would ever work out, especially in a low density population like South Dakota. This whole event also touches on our inconsistent and hypocritical treatment of animals. Dogs are generally cute, fun and smart, so we get upset if we have to put them down, for any reason. But so are pigs, but because we happen to like the taste of their meat, its off to the slaughterhouse. We could all put in the effort to become vegetarians and spare their lives, but we don't. Because...yummy. And it doesn't make headlines around the world.
With regard to your second part, I largely agree about the sexism angle. Sarah Palin bragged about hunting animals from a helicopter, and her soccer mom versus pitbull joke. And Hillary Clinton seemed a little unnecessarily on the blood thirsty side at times. I suspect a lot of that rhetoric was them trying to act tough, thinking it gets them respect. As president, you do have to be tough and often make decisions regarding the risking and taking of human lives, but shooting animals doesn't really relate much to that, IMHO.