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.