I think that a clear argument can be made that the purpose of Greco-Roman myth was to provide a moral paradigm. It was clear that Classical mythology addressed the fundamental issues of human identity and purpose. Greek and Roman modes of thought were concerned with what individuals should do and how they should live. This became a central purpose of Greek mythology:
Greek culture was mythopoetic, based upon myths and transmitted through poetry. These tales had an imaginative character and an emotional one as well. The myths proclaim a truth, which transcends reasoning. These myths try to bring about the truth that they proclaim: the moral truths... The myths dispel chaos. They reveal a structure, order, coherence and meaning not otherwise evident.
Establishing paradigms of morality and truth was of vital importance to Greek culture and was an element that the Romans borrowed in the establishment of their own culture. For both cultures, mythology was a way to articulate codes of moral and ethical conduct. In myths like "Baucis and Philemon," "Bellerophon," and in the mythological reverence the Romans had for forces like Janus, there is a moral order or structure. The paradigm is clear in how individuals must know their position in relationship to the divine. Those who embrace that moral order are praised, while those who go against that moral order are punished.
This moral order is what guided individuals against transgression. For the Classical dramatists (who often took myths as their subjects), transgressors were an example of how not to behave. An example of this would be the way Jason behaves towards Medea, and how she responds. The Chorus is used to accentuate outrage in both instances. Moral responsibility is seen in the pathetic condition of both figures. When Oedipus transgresses against the moral order, he is punished. Aeneas experiences hardship and struggle in the founding of Rome, validating the moral code of sacrifice for something larger. The audience understands that he must take action because the moral structure has been violated. In these instances, mythology provides a moral paradigm in which individuals must submit themselves. Even if they could escape responsibility, there is a clear recognition that the paradigm subsumes them. They must adhere to it. Classical mythology is rooted in the embrace of this moral paradigm, which is meant to guide its audience in action by clearly establishing who we are and what we must do.