Davis is not going to accept a minor league assignment for the simple fact that he may not hit any better down there. Ego wise he cannot take that chance. He is striking out nearly half his plate appearances, he is done. Probably as much mental as physical at this point. At least keeping him around allows the typical fan to say "I can do as good as him", when compared to Davis there is a lot of truth in that, the average guy in the stands really could not play much worse than he is right now.
Sadly with Flanagan, he was one of those individuals who dealt with demons (real or imagined) his whole life and could never overcome it. For most of us who are healthy, it makes no sense, but is very real to the person dealing with depression.