I argue that the motive for seeking out painful art is complex, but what we desire from such art is to have experiences on the cheap--not life experience on the cheap, as one theory puts it, but experiences of strong emotional reactions. Art safely provides us the opportunity to have rich emotional experiences that are either impossible or far too risky to have in our daily lives. We can feel fear without risking our lives, pity without seeing our loved ones suffer, thrills without risking going to jail, and a variety of other experiences that usually come with unwelcome pitfalls. Outside of art, it is almost impossible to have many of these kinds of experiences without completely wrecking our lives--murdering our loved ones, destroying our relationships, being sent to jail, or suffering fatal injuries.
Aaron Smuts, "The Paradox of Painful Art," Journal of Aesthetic Education, vol. 41, no. 3 (Fall 2007) p. 74. Note that Smuts's argument is not that we find rich experience pleasant, but that we desire rich experience even when unpleasant, although we generally prefer for the obvious reasons to have those rich experiences in the least unpleasant ways available.