The kind of people whose songs you've covered from Leonard Cohen to Alex Chilton to Nina Simone are people who have a very fragile muse to them. They are people whose personalities have often been destroyed by their art.
I think that fragility isn't quite as accurate as sympathy, which takes a huge pain threshold. Some people are just born into bodies, born into lifespans that just don't fit anywhere else and they have very little to hang onto to validate and also it's a very lonely thing to notice a certain sense of life and be able to relate that to anyone. It's probably the onset of madness, or it must seem so to the person who has it at the time, who sees the world in a certain way and it usually has a lot of real meaning. Maybe they see spirits everywhere or maybe they divine information from certain happenings and certain peoples that are invisible to most of us, and as a result people deem those experiences not valid and not important, and crazy too, and that can damage a person. Those characters you named have a lot of strength to them even though...There's a lot of strength to the self-destructive soul. Not that it's wise to be self-destructive, but it is wise.