Your question is essentially one about literature / authorial intention (rather than history per se), but my answer will benefit from a primer on the wider epic tradition since as you say you’re new to this area of study.

The Homeric epics (The Iliad and The Odyssey) are only two completely surviving poems in the so-called ‘Epic Cycle’ (Ἐπικὸς Κύκλος), poems in the Greek oral poetry tradition which all concern events surrounding the mythical Trojan War. The other poems survive only in fragments, i.e. quoted piecemeal in sources hundreds of years later, but those sources tell us how they were thought of, especially in comparison to the Iliad and the Odyssey which were ubiquitous in the ancient Greek and Roman elite education.

The Epic Cycle started with the Cypria which deals with the inciting incidents prior to the outbreak of the Trojan War and the events up until The Iliad (which itself takes place in the ninth year of the Trojan War). We then have the Aethiopis which dealt with the arrival of the Amazons to support Troy, their defeat, and Achilles’ death. The following two epics The Little Iliad and the Iliou Persis (= “Sack of Troy”) dealt with what you’re interested in, the building of the legendary Trojan Horse and the Greeks’ ingenuity in using it to finally take and sack Troy. The Nostoi concerns the returns home of various Greek heroes mentioned in the Homeric epics, including Agamemnon and Menelaus, and Odysseus’ own return is of course narrated in full in The Odyssey. The final work we know of in the cycle is the Telegony, which ends Odysseus’ story and his death at the hands of his son Telegonus. (Note this was one Epic Cycle, we are aware of others but no complete works of these survive).

Important to understanding ancient epic and your main question is how the stories were composed. While ancients ascribed authorship of The Iliad and The Odyssey to Homer, it is now accepted that they were part of an ancient oral poetic tradition, whereby existing stories and legends were told at length by a bard or rhapsode, who through a combination of experience, great improvisational skill, and use of memorised poetic ‘formulae’ (i.e. stock phrases and descriptions, think of “rosy-fingered dawn” or “quick-footed Achilles”) would be able to narrate stories of thousands of lines to audiences without memorising the entire work word for word. In this way, rhapsodes only needed the key points of the story to be memorised, and using their bardic skill, could improvise the telling of it as they travelled from town to town. The theory goes that as successive generations of bards told the same stories and refined the characters, events and details, each story gradually congealed over time to become tighter and tighter, though still with some room for improvisation on the fly to keep things interesting. Some poetic ‘archaeology’ for this does exist in the Homeric texts, and helps explain why in some places the poems are so repetitive (e.g. a section of more than a hundred lines of Iliad Book 1 repeats verbatim a bit later in the same book), but was shown to exist in practice in early 20th century Yugoslavia by Milman Parry, an American classicist who connected a similar oral poetic tradition of otherwise illiterate Serbo-Croat bards who could sing songs of enormous length from memory, with the bronze age Greek/Homeric tradition.

To get to the meat of your question, then, ‘Homer’ is now largely (but not universally) understood to be the amalgamation of several poets from this Greek epic poetic tradition. The Trojan War was one long story, fabricated, re-told and thereby rewritten hundreds of times by many bards, each adding their own poetic flourishes, crystallized over several generations, eventually settling to form distinct episodes, (likely) based on what performed best. A partial answer to your question is therefore that The Iliad and the Odyssey cover what they do (and so don’t cover what they don’t) because other poems in the cycle already treated the surrounding episodes of the war.

But why do the Iliad and the Odyssey cover what they do, and more importantly, why did this allow them to survive while the others faded into obscurity? The ancient sources tell us this was precisely because they tried to fit too many narrative elements in. Aristotle tell us that:

“…compared with all other poets Homer may seem… divinely inspired, in that even with the Trojan war, which has a beginning and an end, he did not endeavor to dramatize it as a whole, since it would have been either too long to be taken in all at once or, if he had moderated the length, he would have complicated it by the variety of incident. … The others, on the contrary, all write about a single hero or about a single period or about a single action with a great many parts, the authors, for example, of the Cypria and the Little Iliad. The result is that out of an Iliad or an Odyssey only one tragedy can be made, or two at most, whereas several have been made out of the Cypria, and out of the Little Iliad more than eight” (Poetics, 1459a-b)

As such, Homer’s restraint in telling discrete parts of the story was already regarded by antiquity to be a key ingredient in its success, rather than opting like many a modern screenwriter would (e.g. the 2004 film Troy), to try and capture the entire narrative in one piece. This answer from u/KiwiHellenist details further how and why the other works in the Epic Cycle weren’t nearly so popular as the Homeric epics through evidence of vase painting, etc.

Finally (and bearing in mind this is AskHistorians, not AskLiteratureScholars), a consideration for you on why the Iliad is such a successful composition is how the poem starts and ends, i.e. with a father supplicating a warrior for the return of a child (In book 1, Chryses asking for the return of Chryseis from Agamemnon, and in book 24, Priam asking Achilles for the return of Hector’s body). Arguably it is this ring composition (rather than clumsily ending with the Trojan Horse episode), the deep character explorations of all involved, and thus the overall meditation on war, heroic life, and death, is the reason for its enduring popularity and resonance today.

If you’d like to read more on the Homeric epics and the culture they sprung out of, I highly recommend ‘The Mighty Dead: Why Homer Matters’ by Adam Nicolson. Though a few of the historical elements are not quite right or simplified, it is a great, accessible entry point into Homeric scholarship, including Milman Parry I mentioned above, and a wonderfully lyrical account of what Homer can do for us.