There are probably three things at play here. First, there is the centrality of hospitality in Greek society, second, the need for repetition during the poem to make it easier to recite these stories, and finally the importance of just compensation for your actions in the epics.

The first is the concept of xenia, or hospitality, was very important in Greek society. The rights of guests and hosts were protected by Zeus. throughout the story, in both the Iliad and the Odyssey, being a bad host or a bad guest has dire consequences. Just consider the fact that the entirety of the Trojan War happens because Paris is ostensibly a bad dinner guest. Being a good host (and guest) on the other hand helps strengthen alliances and morale. Emphasising that everybody got their fair share is thus an affirmation of xenia.

The second, more practical reason for verbatim repetition in the epics is that they were recited verbally in front of a live audience, off the top of the poet's head, all in a fixed meter (dactylic hexameter). Since its impossible for a poet to know such a long poem by heart, certain portions of the poem, like descriptions of feasts, are repeated throughout the poem verbatim to make sure that the poet has some time to think about the next part of the poem while describing a certain scene, like a feast, on autopilot.

Lastly, and this is more speculative on my part, but related to xenia, are that the concepts of honor (tîmê) and worth (arete) are central to Homer's Greece. In living, and especially in battle, the goal is to be worthy or excellent according to the metrics of society. For example, fighting bravely or coming up with a good battle plan. This creates a ranking, a hierarchy, of soldiers; the braver and better you fought, the more you are worth. It is of central importance that you are justly compensated for your honor, in the form of prizes handed out at the end of the battle. The story of the Iliad centers around such a case of unjust compensation (or rather, by taking Briseis away from him Achilles loses part of his worth and his place in the hierarchy of men is unfairly diminished). Just like everybody is owed their fair share of the booty at the end of battle based on how honourable they fought, getting your fair share of a a meal is a reaffirmation of your place in society.

Sources:

For a short description of some of the Greek concepts, check here.

Part two and three of [this lecture series] (https://www.thegreatcourses.com/courses/iliad-of-homer.html) by Elizabeth Vandiver go into both the Homeric question (How was it recited? Who wrote the epics? What is the role of repetition) and the themes of honor and worth.

And finally I looked at Amanda Urban's "What Pains are Fated to Fill Your Cup: The Role of Food, Drink, and Xenia in the Homeric Epics" for background information on xenia.