Everyone else here has already pointed out the (sorry, OP) obvious main reason for Odysseus’ disguise: he needs to see what the situation is at home and figure out how best to dispatch the suitors — and anonymity permits him to do this. Let me add a few other factors:Part of Odysseus’ heroic identity is his skill in dissembling and lying and confabulation; dramatically, this offers the audience a revenge built on this particular hero’s specific charisma.It allows for one of the most moving moments in ancient literature. Only one being recognizes Odysseus at first sight, disguise or no disguise: his dog Argos. The ancient dog is so overjoyed that his heart explodes and he dies. I cry every time I read it. (In Greek, it’s hard to take.)It also allows for another great recognition scene: the great moment when his childhood nurse, Eurykleia, recognizes him by his scar as she bathes his feet. Odysseus has to grab her by the throat to stop her cry of surprise and joy, then swear her to silence. The scene is masterfully constructed and includes a brilliant flashback to the childhood hunt when Odysseus got the scar.So besides the obvious strategic motive Odysseus and Athena have, there is the concinnity of the disguise with the hero’s identity, and the affective motive of the storyteller: the disguise heightens the power of the recognitions, when they come. To see the beggar string the bow and slaughter the suitors — does any revenge story compete? More to the point, is any revenge story uninflected by this one?
