Once again, misunderstood 
I was communicating Alastair Roberts’ view, not my own.
I agree with you, and have done my own fairly extensive reading of (translated) original sources and secondary sources. My conclusion is that there is very little support for understanding headcovering as cultural. The writings of present day non-Christian historians rarely support the cultural view, though the changes to their conclusions about veiling over time don’t speak well to the reliability of their conclusions for our purposes :).
As much as I like Bruce Ware, after tracking down the sources he cites, I could not see how they support his arguments at all (if you are aware of them). His writings recieved virtually no attention outside of Christian circles last time I looked. But again, does that matter one way or the other?
My understanding is that headcovering, even though it is misunderstood, should still be practiced, even as the Lord’s Supper was still practiced in light of accusations of cannibalism.