The mandates or permissions of any religion are always measured against civil law. We don't accept multiple married partners, nor child marriage, nor beating a spouse, nor sequestration in the domicile, nor child labour, nor keeping a child away from an education, although there are religions that think these actions are just fine.
Hiding the face is a male way of preventing other males from viewing his property and is purely and simply a statement of male possession.
Hiding the face is, I understand, not mandated by the religion, it's a custom only in one small, and very backward, area of the Muslim world. When working as a surgeon in Bosnia civil hospitals I asked if they had restrictions on examining female patients: "We aren't all third world, you know," the local physician indignantly burst out.