In Mohammed's day, only his own wives were required to wear niqab and that was after his death. This desire to wear niqab is in part, a desire to be "holier" than their sisters who only wear hijab.
I suspect it's more about control by their husbands than their own wish. In the Alhambra in Spain, there's a carved stone fountain that looks a bit like a birdbath - free-standing, shallow, dish-shaped. One of the Muslim rulers thought that his favorite wife was getting too friendly with one of the eunuchs who monitored his harem. He had the eunuch killed, and had the fountain filled with boiling lead and made his guards push her face into it.