Should an audience always relate to the downfall of a tragic hero moralistically?
Like Oscar Wilde said once, art does not advocate to morality or immorality, but to art itself. In that same note, if a work of art is well-written (he would also say) it would produce in the reader the exact sentiment that the author seeks to provoke.
This being said, I would not say that one should "moralistically" relate to a character, but rather emotionally OR philosophically. For example, I cannot help but feeling sorry for Macbeth.
If we were to make the mistake of examining the play moralistically there would be a lot of interruption in the development of emotions in the reader. However, if we take it from a psychological and emotional perspective, one cannot deny that the man did what he did out of a disoriented and sad psyche that consumed him to the very end.
Therefore an audience may or may not relate to the downfall of a tragic hero, but a big difference occurs when the author provokes emotion and psyche in the reader.
When reading any of the "tragic hero' stories, the "tragic" element usually implies a varied amount of occurances and situations that are at a heightened, dramatic tone. These tragic moments deal with larger, more complex or biblical questions or examples of morality.
Do we feed badly for Oedipus at the finale of Oedipus Rex, or as an audience, have the thoughts of ignorance, deceite, and ego been provoked? Any mortal can morally relate to all three of these themes. And if not, maybe they realize they have through education and readings like this.
So the question is not whether or not the audience should always relate to the tragic hero moralisitcally, but should their moral compass or the overarching canon of moralistic questions be evoked through the story of the tragic hero? Then the answer is yes, as that was, at large, the premeditated expectation with tragic hero tales.
Further Reading: Oedipus Rex by Socrates