Homer is endlessly interesting because he's so influential, and yet so insubstantial. By this I mean the Iliad and Odyssey are the two most influential, long lived texts in the western tradition, and yet we have nothing to say with any confidence about the person whose name is attached to them. Classical Greek writers - Plato, Aristotle in particular - talk with confidence about Homer. And whatever the myth or reality that accrues around the name, the name itself holds enormous sway over all Latin and European literary culture.
George Chapman's 1616 translation of Iliad and Odyssey include a lengthy preface in which he excuses the great amount of "death" in Homer, because he is a compendium of life. It had been only a century or so since knowledge of ancient Greek was revived in the west, and Homer seemed to be suddenly brought to life, in his own language, instead of Latin paraphrases and translation. And coinciding with Chapman's 1616 translation, there was a renewed philological interest in early forms of English. And so Chaucer became the "English Homer" - the inventor of English poetry. So Homer becomes a convenient figuration for the beginnings. The myth of Homer endures because it provides a stable point of origin for that whose origins are irretrievably lost. And even if it does no real good to insist on an author for the Iliad and Odyssey, the fiction of Homer does no real harm either.