Another reason Achilles' death is left out of the Iliad is because the Iliad was not a "stand-alone" poem. In antiquity, there were several different poems that made up what has become known as the "epic cycle." So, Homer's Iliad is just one of about six lengthy poems that would have made up this "epic cycle." The death of Achilles appears to have been dealt with in a poem by Arctinus of Miletus entitled the Aethiopis.
Homer's Odyssey is another part of the "epic cycle." Notice that Odysseus' death is also not described in this epic. This event seems to have occurred in another poem, which was entitled the Telegony.
Homer's Iliad is one of the West's greatest epic poems, whose conventions were established using heroic characters, the participation of gods and goddesses, the grand style (including epic similes), beginning the poem in medias res, and the invocation.
Among the Iliad’s myriad legacies, two are especially important for the history of literature, which prevent Achilles being killed. The first enduring legacy is that heroism is defined in the poem as fighting hand-to-hand in battle—like the gunfights on Main Street in later Westerns. Considerations for family and community come after that for one’s own reputation. Hector, who is a very good man, nevertheless chooses his own dignity and integrity over that of his community and his wife and child. As Moses Hadas points out, "heroism for the ancient Greeks was an individualistic quest, and the hero’s ultimate loyalty is always to himself, not to his family, nation, or even his gods."
The second enduring legacy is Homer’s treatment of the enemy—the Trojans—as equal in dignity and humanity to the army of Agamemnon and Achilles. Both armies speak the same language, worship the same gods, and live by the same codes. The Trojans can be seen as more sympathetic, since we see them with their families, while the Achaeans are an army on the prowl. The critic Northrop Frye says that the demonstration in the poem that the fall of an enemy is as tragic as that of a friend or leader gives a disinterested quality to this literature which is part of its authority, moving it beyond entertainment, propaganda, or devotion toward “the vision of nature as an impersonal order.”
Thus his death would prevent these from coalescing.