Sister, obviously I am not asking you to concede to what I have mentioned. I wrote what I know, understand and believe. Now it is up to you to accept it or reject it, cause in the end, Muslims are responsible of own knowledge, understandings and beliefs. I believe what I wrote is true and logical, but if you think what I wrote is untrue than be it for you. No persuasion other than discussion and pointing out the facts according to knowledge one have. 
Well, I think you should re-read the commentary by Maududi and re-assess what you wrote, as what you wrote contradicts what Maududi wrote, even though you are referring to Maududi writing. Maududi in that commentary mostly wrote situation before surah was revealed, not about situation at the time surah was revealed… plus he also wrote that Jews in Madina were living separately from Muslims, … hence living separately, there was little chance of intermingling at public places and molest women of each other.
Nevertheless … here is what I know (that you can confirm):
When Prophet (SAW) migrated to Madina, in Madina, there were mostly Arabs and Jews. Arabs accepted Islam (though there were some who were Munafiqs too … but you can consider them Muslim in practical sense, as they were acting as if they were Muslims).
As for Jews, there were few tribes in Madina (I think, 5 different tribes … 3 big and 2 small or insignificant). Three were big and quite powerful tribes, and they were Banu Nadhir, Banu Qaynuqa and banu Qurayzah. Each tribes had their own area where they used to live.
Two of these tribes, Banu Nadhir and Banu Qaynuqa got banished from Madina before gazwa-e-Khandaq. The remaining big tribe, Banu Qurayzah got terminated just after gazwa-e-Khandaq.
Surah al-Ahzab was revealed after gazwa-e-Khandaq … and it means, after 3 of the main Jews tribes were either banished or terminated.
It also means that Madina after termination of Qurayzah became overwhelmingly Muslim city, though even before that, when all Jews were living in Madina, Muslims (who were mostly of Arab descent) were living separately from Jews.
So … when Muslim women were getting teased and molested, the person teasing or molesting were Muslims (where Munafiqs are included, as for Muslim society, they were Muslims).
It also mean women the ayah is talking about, women who were getting molested in public places, were Muslims, and molesters were Muslims too.
So, for a woman, to wear a certain type of dress to declare that they are Muslim become meaningless … because in the area they were living and moving around, men and women, all were Muslims anyhow.
Thus to say that women were told to put on niqab so that they can be recognized as Muslim is ridiculously funny. It is just like saying that in a society where all (each and every one) are Pakistanis, one is wearing Jinah cap to get recognized as Pakistani. :). It is just like, in a gathering of 100 donkeys, one donkey has a poster on his back saying that he is a donkey.
So, to me, it is obvious that the ayah does not mean to say that by wearing certain dress they would get recognized as Muslim (as all were Muslims anyhow), but ayah says that if they do not cover their face then people would recognize them (as someone they know or not) and thus would not molest them.
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Well, I never said that what Muslims (men and women) wear on Hajj, is dressing code for Muslims.
Actually, I mentioned the word ‘Aurah’, that is part a Muslim male and female should cover in public, as minimum dressing requirement, and that is what Muslim men and women wear during Hajj … as that is what Allah desires from Muslim men and women. It does not mean Muslim men and women could not were cloths that cover more than ‘Aurah’. Normally they do.
I mentioned Hajj dressing to say that … if niqab was desired and required by Allah for Muslim women, than that requirement would have been during Hajj too … as requirement in Hajj is to cover what Allah wants Muslim men and women to cover minimum. If Allah forbids covering face by women during Hajj, it means that covering face is not requirement from Allah …
But then, if a woman is having complex about her looks, or women with dubious character wants to hide her face in public than she has all right to hide her face if society do not consider that abhorrent, no problem. Some women can hide their face for whatever reason they find it fit, that is also no problem.
Only thing I am saying is that, hiding face (with niqab) from public is nothing to do with Islam, that is all.