Recently I ran into a presentation on chapel veils from 2016, in which he gives the scriptural and doctrinal background of chapel veils.
The point he makes is that while there is scriptural authority and traditional support for chapel veils in the Catholic Church, their use fell out of currency after Vatican II, and there is no requirement that Catholic women wear them in OF, EF, or DW mass. Beyond that, there's the question of whether women who wear them want to single themselves out in some way over and above accepted and prudent ways to dress during mass. If women want to use them for some sort of ostentation, it would be good to have second thoughts.
One thing that puzzles me is that, in 30 years as an Episcopalian, I must have gone to mass at roughly two dozen parishes, and I never saw a chapel veil. Certainly some women wore hats, as many women do at our Catholic parish, but that would be a much more down-to-earth way of covering their heads, less ostentatious, and less more-Catholic-than-the-Pope. But if chapel veils are part of the Anglican patrimony at all, it's not a very big one, and certainly optional.
So I'm not sure what the big deal is about chapel veils in the OCSP. It seems as though some "restorationist" Catholics, those who want to go back to some ideal time before Vatican II, have adopted Anglicanorum coetibus as some sort of ally in this fight. The observers I've talked to think there may be a tendency in the second tier of OCSP parishes, like the ones in California, to attract millennial "restorationists" to replace the disaffected Anglicans who haven't been much attracted to the project.
This may be the explanation for why, as my regular correspondent pointed out, there were no chapel veils to be seen in the early shots of the Pasadena group in yesterday's post, while in the recent shot, the only woman visible in the much smaller group was wearing one.
