This is a reflection on this text.
The Ba"kh (ב"ח), standing for the Bayit Hadash (בית חדש), was written by Rabbi Joel Sirkes, who lived in Poland, from 1561-1640. This work is a commentary on the Arba'ah Turim. His other work includes commentary on the Talmud, two works of responsa, and a commentary on the book of Ruth.
One of the things that I noticed playing a very strong role in his comments, as well as in the comments of the Mordechai, whom he quotes, is the force of communal practice. The thing that establishes what is permissible to wear is what is the norm. The norm in his community, like that of the Mordechai, is that "בתולה הרגילה בגילוי שער ", a "virgin... is
accustomed to revealing her hair", and therefore "לא חיישינן, דליכא הרהור", "we are not concerned, because there is no [concern
over] improper fantasy".
When taken in a modern light, I'd end up taking this approach to mean that since women don't generally cover their heads in our (American) society, they don't need to- even married women. I've seen modern writers and rabbis take this approach. It has a certain loyalty to one meaning of modesty, from the perspective of not standing out, not drawing attention. At the same time, I don't know which communal norms I should be judging by, in the modern world. The local general community? The local Jewish community? The Jewish community/movement with which I prefer to affiliate? Depending on the answer, I'd come out with very different practices. That sort of difference didn't exist in Rabbi Sirkes' time.
On the other hand, he also handles a variety of texts from the Talmud that deal with issues of women's modesty, and hair-covering in particular. These establish a textual requirement, beyond the impact of social norms.
One thing that I like about this text is that it explains a clear tension on the issue of unmarried women's headcovering, and addresses it from both textual and social angles. It shows how complicated the issue can be.