When we looked at Shulhan Arukh Even Ha'Ezer 21:2, I really only addressed the main text, that by R. Yosef Karo... Today, I opened up the book to see if I'd missed any comments by the Rema on that halakha.
There's nothing. Not a word.
In other words, this is something where Sefardim an Ashkenazim were in agreement. When the Rema wrote his gloss to adapt the Shulhan Arukh for Ashkenazi audiences, he didn't have anything to say to alter what he saw on the page. That speaks pretty loudly, to me, for a community whose current practice is for unmarried women to go sans any head-covering, almost across the board (I know some Haredi communities have unmarried women braid their hair, a la the other interpretation of BaMidbar 5:18, where the term "" means to 'unravel one's hair', i.e. braids, rather than 'uncover one's head'). However, if the same source phrase was supposed to mean different things for married and unmarried women, you'd think that a halakhic text would say so explicitly.
How this came to be is a real mystery to me, for all that the usual theories have to do with the practices of surrounding cultures. Nevertheless, the "uncovered head=unmarried woman" equation is deeply coded into current Ashkenazi culture, and putting on a head-covering for the first time after you get married is a big deal. Heck, it was a (quiet) big deal for me, and I'd been wearing a kippah/etc for over half a decade already.
So I am all in favor of a broader sort of head-covering practice for women as well as men (someday, I'll start talking more about men, kippot, and the like), but I don't want to deprive people of a social practice that speaks to people so deeply. I liked my own transition from kippah to full-head covering. But would it work more broadly? Is this a change worth pushing for, for that matter, or is it just a spiritual practice that works for me, and shouldn't be socially supported?