You wrote:
“It would be more to the point for the priests there to simply prohibit inappropriate attire at Mass.”
Actually no. When a woman wears a veil she is much more likely to be modestly dressed. What the priests are trying to do is not force a whole series of dress rules on the women. No, instead, what they’re trying to do is create a new outlook about dress at Mass by insisting on a visible sign of humility (the veil). That’s how it always worked for centuries.
According to a footnote in my Challoner-Rheims version of the New Testament, St. Paul ultimately appeals to the authority of custom in 1 Corinthians 11:1-16 to justify his position on women covering their heads in church. (Certainly Bishop Challoner’s interpretation of Scripture must be just as valid as hfr’s.) St. Paul’s argument was appropriate for the time and the culture in which he lived because at that time, women were seen as inferior and subordinate to men and as needing to veil themselves in public as a sign of this inferiority and subordination. However, the advice which he gave to the Churches of Corinth in the first century no longer applies to the Church in this century because the status of women and custom have changed.
The Church’s rule that women cover their heads at Mass was not a divinely ordained rule (like the male priesthood), it was not a Tradition with a capital “T”. If it had been, the Church would not have changed it. It was, in fact, an external aspect of the liturgy, which was changed when the times changed.
Priests should certainly exhort women (and everyone else as well) to dress appropriately for Mass but it isn’t necessary for them to demand that women cover their heads in order to achieve that end.