Does there have to be hamartia in Modern Tragedies?
As defined in Aristotle's "Poetics," the evolution of a character from one that rests in nobility to one of destitution from their own character flaws is an essential component of Ancient Tragedy. Most notably seen in Oedipus, but also present in other Greek characters such as Bellerophon, Heracles (to a lesser extent), Achilles, or Creon. The element of hamartia was a part of Aristotle's definition of tragedy that involved some level of moral evolution or the type of emotional journey that was to be undertaken by the protagonist. In Artistotle's mind, this element of transformation represented the best of tragic conditions. The modern conception of tragedy still takes this aspect in mind, but it also explores it in a variety of ways. For example, Goethe's Faust and Flaubert's Madame Bovary are tales of tragedy where hamartia is present in both protagonists. Yet, this is not the only component of the tragic condition in both works, as tragedy involves much more in terms of both characters and social setting. Beckett's Waiting for Godot is still tragic on many levels but strives to move away from a fixed notion of tragedy. In modern tragedies, the concept of hamartia may still be a component, but it is not as defined of an element as it was by Aristotle.
'Hamartia' as referred to by Aristotle in his Poetics is an 'error' or 'flaw' that makes the tragic protagonist a victim of fatal circumstances. Oedipus killed Laius and became the king of Thebes and married Laius's widow, Jocaste, without knowing that he had committed an error of killing his father and marrying his mother for which Thebes had to suffer from plague.
'Hamartia', meaning 'beside the mark', was a term that Aristotle borrowed from the field of archery; it was an error born of 'hubris', i.e. 'pride' which goes before a fall. It was an intellectual error, not a moral failing. A towering personality belonging to high station like Oedipus or Agamemnon was still prone to such error leading to reversal of fortunes.
In modern social drama, e.g. Galsworthy's Justice or Arthur Miller's The Death of a Salesman, 'hamartia' does have little significance. The protagonist--a junior clerk or a humble salesman--pitted against a cruel society is too ordinary to be capable of any such intellectual error, that also born of exceeding self-consciousness. This absence of 'hamartia' may also be the reason why the protagonist in a modern social tragedy tends to be more pathetic rather than tragic.
No, "hamartia" does not have to be part of modern tragedy. But it might help if you understood this concept outside the formal sphere of Poetics and saw it instead as something common and as widespread as it is. Hamartia is usually defined in English as "a fatal flaw," but it would help if you knew that the word is still in use today. Αμαρτία is defined as "sin" in even something as simple as Google Translate. The root of the word is μαρτυρώ, which means "to witness," and is linked to the English word "martyr."
How many people do you know why have something self-destructive about them that they can't control and that gets them in trouble? How many stories in movies and books exist where the protagonist does something stupid to get themselves in trouble? In stories without a happy ending, how often is it this problem in themselves that brings them down?