I believe the manner of Zainab's marriage to Mohammed sent shock waves among the Arab women who detested the way the Prophet broke up a loving relationship of Zainab with Zaid (Mohammed's son in law). They all decided to go INVISIBLE to be safe from Mohammed's eyes. Later it became "hiding your face from EVERY MALE MUSLIM for fear of being abducted or raped."
The custom has spread far and wide by now. Many feel that burka should be banned in the West since it makes the Muslim females invisible with the result that Muslim males seduce the non Muslim girls quite eaisly who are visible and freely approachable. Mohammed did not trust his followers with the women. Hence he made act of worship an all-male affair.
Only recently a few Muslim females have entered the mosques to be seated at the back or behind screens as a tiny step towards equality. It is for the West to remove the FEAR of males from the Muslim females and encourage them to cast off the burka and be equal to the non Muslim females.