The extent of covering has been linked to social status for millenia. Perhaps the prohibition of niqab and "gloves" (quffaz were more like mittens), were a female version of ihram- a simple dress that eliminates markers of social status. I'm not going to argue whether it was indeed forbidden during Hajj, but if it was, perhaps it was to break down barriers of social class, much like the fact that men do not conceal themselves from public view during Hajj, regardless of their status, but when they return to normal life, no one gets to see them without intermediaries.