The law you advocate has been in existence since Prophet Muhammad's time.  Wearing niqab (a face-veil) is not "wajib" (mandatory), per authentic Shari'a, still less the burqa, which is an Afghani cultural innovation, and a religiously unwarranted one--a "bidah", if you will.

Hijab is wajib, not niqab.  That Salafis and other wahabbi-derived maniacs force women to wear niqab is merely another aspect of their extremism.  Nonetheless, pious women have for the sake of modesty been wearing face-veils since at least the time of Is'haaq son of Abraham (alayhimus-Salaam).

But (at least) since the advent of the Muhammadan dispensation of Islam, it's been voluntary, not required (per the authentic tenants of the Faith).  The practice is recognized as "mustahab", i.e. salutary, not mandatory.

There is NO Islamic law prohibiting a woman from baring her face for identification purposes to lawful authority.  Extremists on both sides of this issue seem to delight in promoting needless conflict.