Why does Homer refer to Agamemnon's return from Troy in Books 1-4 of The Odyssey?
This is an interesting question, in that it assumes the Homer was in control of his story, and had intentions about what he was imparting to his audience -- which may or may not be the case. Homer, about which we know almost nothing, may or may not have composed the Odyssey. It may have been the work of many bards over the centuries, and Homer, possibly, was the one whose version of a well-known tale came down to us. So any assumptions about intention of the author (which are dangerous even when we are talking about well-known authors or authors that are alive today) is fraught with peril. So bringing up "why" opens a can of worms.
This aside, we can look at it purely from a storytelling point of view. If the Odyssey is the "sequel" to the Iliad, then there is a gap in the storytelling between the end of the Iliad and the beginning of Odyssey. The Iliad covers only about a 50-day span in the tenth year of the Trojan War. It does not address two major things that happened before the beginning of the Odyssey: the fall of Troy, and the departure for home of the Greek army (including Odysseus). Since Agamemnon was the supreme leader of the Greeks, his return home, and what happened after that, was an important part of the story of the Trojan War. If we are going to ascribe motives to Homer, it might be that his audience demanded to know what happened to the character of Agamemnon, since he was such a large actor in the story up to this point. Also, the story of Agamemnon's demise is the subject of a very famous trilogy of plays by Aeschylus, the Oresteia. While this work was from the fifth century BC, at least 200 years after the Odyssey was first written down, the story of the Oresteia is very old; perhaps as old as the Iliad and Odyssey themselves. In fact, the plot of the play Agamemnon is largely contained in the Odyssey, although there are other versions and the play itself contains details not told in the Odyssey. Greek poetry and drama, as English drama, poetry, and literature today, often refer to other stories outside of the main one that people of that culture are familiar with.
In Books III and IV of the Odyssey, Homer has at least two fairly clear reasons for bringing up Agamemnon's sticky end. In Book IV, Telemachus is talking to Menelaus, Agamemnon's brother; it seems obvious, when Telemachus is asking Menelaus what happened when the Greeks, including Odysseus, returned from Troy why Menelaus would tell the extraordinary tale of so close a relative of his. But in Book III, when Nestor brings up Agamemnon's end, there is another reason. It's a neat bit of literary irony, and a sort of sop to Telemachus' ego at being fatherless:
No matter how far out of the world you live, you will have heard of Agamemnon and the bad end he came to at the hands of Aegisthus—and a fearful reckoning did Aegisthus presently pay. See what a good thing it is for a man to leave a son behind him to do as Orestes did, who killed false Aegisthus the murderer of his noble father. You too, then—for you are a tall smart-looking fellow—show your mettle and make yourself a name in story.
Nestor is telling Telemachus that it is good he was at home to guard Odysseus' house and wife until he could return from the wars. This soothes Telemachus somewhat, and makes it easier for him to continue on his quest to find out what happened to Odysseus.