Part of what makes the Illiad and the Odyssey so interesting is that they are pieces of history.
Yes, in that Homer was a real person, living and writing around the 8th century BCE. But, this is not a biopic about Homer....
Not the narrative obviously, but as documents of the beliefs and norms of a culture long since passed. Nolan's disinterest in even the basics of clothing is a big turn off to me for that reason. It's a cultural artifact! Put a little culture in the movie!
Problem: The Odyssey is set supposedly in the 12th century BCE, some 400 years before Homer was born. And, I don't recall Homer being too specific about the clothing and armor being worn. Nor was his an age with tons of scholarship about the clothing of people 400 years before Homer.
And, in fact, the stories he collected and reworked into his Odyssey are set in about 1200 BCE, but are actually from a
variety of times from before Homer.
So, whose clothing do you use? That of 1200 BCE? That of 800 BCE? That of whatever little you can glean from the text, which would probably be Homer's
guess at what people wore 400 years before? The best guess of scholars for what would have been historical to the times of the first versions of each of the sub-narratives used?
The work is a part of history, but it is not a work describing historical events. So what passes as appropriate for costume is... arguable.