I have a question for you QM, what is the state of Illuminata's head covering industry? Given this world's remembrance of ancient humanity, are hats present, and if so what kinds? Do iron-tamers wear cowboy hats? Do sword-machines wear knight helms? Does Egophage wear a version of a night vision/scope headset? Do Koinon artillery shell factory owners wear top hats? Do Koras weave flower crowns to give to each other?
Hats were originally useful for protection from UV rays, dust and from the cold. This was never relevant on Illuminata, where clothing has more of a ceremonial function. You may have noticed some of the temperature descriptions are bonkers - temperatures rise to sixty-degrees celsius in Deluge on average. But this is not something the characters really are concerned about, because their bodies are not very biological. You all just like playing dress-up and feeling human doing so.
Usage of hats becomes a question of utility and style. In Kora's Progeny, hats are deeply disliked - hoods which don't ruin your hair are much preferred. Because hair in the Progeny is itself such a powerful augmentation, the hair is usually the epitome of style, and ornaments are woven into the hair - Sympathy's own extremely intricate style is a non-euclidean bun only possible to create with psychic power. In war, you're going to be wearing treated armor of petrified molted skin, what was already called "bark-armour" in a prior update. It looks superficially similar to Eldar wraithbone, but is of course not a psychic but a syntho-biotic construction made from the hollowed out dead or specially printed hollow bodies.
In Titanagalbat, there is a preference for holographic shawls and veils for brides. Mulberry's use of a loose head-covering is a sign of her freedom - it is expected that both male and female brides in Titanagalbat will cover up and reveal their faces only to the titan and those closest to them. You would have spent much of your life not seeing the faces of your fellow menials.
Helmets and other utilities in warfare are popular. In Koinon, for example, most are going to be going into battle
wearing something similar to a Corinthian Helm, with necessary modifications for being in the 30th and not the -1st millennium. But there isn't a lot of armor that can protect you more than the carapace you already have, and so there is a preference for form over function. Egophagic outfits, where you're needing to wear thermoptic camouflage,
can get quite outlandish.
Chrome Kings don't necessarily like wearing head coverings because they want to feel the wind in their hair and it can fuck with their dread-locks, which they use to plug into machinery.
But keep in mind that Illuminata also goes through hatful and hatless eras. These are important epochs marked by major events. It may well be that Illuminata will soon re-enter a time of hats, much to the dismay of your Procrustean Locks. All should fear the dawn of the hatted sun.