Why Is Niqab Not Allowed in Hajj?
Question

According to the answer to question no. 172289 , it is not permissible for a woman to wear the niqab or gloves when in ihram, as is indicated by the hadith. But you said that, despite that, she must cover her face with something else, other than the niqab or burqa‘ (types of face veils). My question is: if covering the face is essential, then what is the problem with using the niqab?
Praise be to Allah.Can women wear niqab in hajj?
The Messenger (blessings and peace of Allah be upon him) forbade woman in ihram for Hajj or ‘umrah to wear the niqab and gloves. (Narrated by al-Bukhari) 
There is no report to suggest that the Prophet (blessings and peace of Allah be upon him) forbade the woman in ihram to cover her face , or that he (blessings and peace of Allah be upon him) instructed them to uncover their faces. 
Hence women in ihram at the time of the Prophet (blessings and peace of Allah be upon him) used to cover their faces with something other than the niqab when non-mahram men passed by them. 
The prohibition on women wearing the niqab and gloves means that they should not wear a separate garment that is made to fit the face and hands. It does not mean that they should not cover them at all.
This is similar to the ruling of the Messenger (blessings and peace of Allah be upon him) forbidding the man in ihram to wear a chemise or pants. This does not mean that the man should remain naked; rather he should cover his body with the izar (waist-wrapper or lower garments) and rida (upper garment). 
Why is niqab not allowed in hajj? 
Men are prohibited to wear garments that are made to fit the body, and they are instructed to cover their bodies with other kinds of garments. Similarly, women are prohibited to wear the niqab and gloves, but they should still cover their faces and hands with something else.
Ibn al-Qayyim (may Allah have mercy on him) said: 
“The Prophet (blessings and peace of Allah be upon him) did not prescribe for the woman to uncover her face in ihram or otherwise. Rather there are texts which prohibit the niqab in particular, just as it is prohibited to wear gloves, and it is prohibited to wear a chemise or pants. It is well-known that the fact that he prohibited wearing these things was not intended to mean that they should remain uncovered and not be covered at all. Rather the scholars unanimously agreed that a man has to cover his body with the rida and izar. 
So how can the meaning of the text be exaggerated and taken to mean that it is prescribed for a woman to uncover her face in the midst of a huge crowd? 
What text, interpretation, general meaning, and knowledge or interest would dictate that? 
Rather the woman’s face is like the man’s body: it is prohibited to cover it with a separate piece of cloth that is made to fit it, such as the niqab or burqa‘ . In fact, it is prohibited to cover it with a separate piece of cloth that is the size of the hand, like the gloves . As for covering the hand with the sleeve, and covering the face with the headcover or garment, that is not forbidden at all.” (Badai‘ al-Fawaid, 2/664-665) 
It says in Fatawa al-Lajnah ad-Daimah (11/1920193): 
“The woman in ihram for hajj or ‘umrah should not wear a niqab or gloves , until she has gone through the first stage of exiting ihram. Rather she should let her headcover come down over her face if she is worried that non-mahram men may see her. But that concern is not ongoing, because some women are alone with their mahrams. Those who cannot be away from non-mahram men can continue to let their headcovers come down over their faces, and there is no blame on them for doing so. By the same token, they can cover their hands with something other than gloves, such as the (sleeves of) their ‘abayahs. And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and Companions. 
Shaykh ‘Abd al-‘Aziz ibn ‘Abdullah ibn Baz, Shaykh ‘Abd ar-Razzaq ‘Afifi, Shaykh ‘Abdullah ibn Ghadyyan, Shaykh ‘Abdullah ibn Qa ‘ud.”
Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him) said:
“What is meant by “women should not wear the niqab or gloves” is that they should not wear something that is made to fit the face, such as the niqab, or to fit the hands, such as gloves. It does not mean that a woman should not cover her face and hands, as some people imagine. It is obligatory to cover them, but with something other than the niqab and gloves.” (Majmu‘ Fatawa Ibn Baz, 5/223) 
Shaykh Muhammad ibn ‘Uthaymin (may Allah have mercy on him) said in ash-Sharh al-Mumti‘ (7/165): 
“There is no report from the Prophet (blessings and peace of Allah be upon him) that forbids the woman to cover her face; rather it is narrated that it is not allowed to wear the niqab [when in ihram], which is more specific than covering the face, because the niqab is a garment made to fit the face. It is as if women were forbidden to wear garments made to fit the face, as men were forbidden to wear garments made to fit the body.”
Thus it is clear that the reason why the woman in ihram is forbidden to wear the niqab is because it has been made to fit the face. Therefore the scholars said that the woman’s face in ihram is like the man’s body. 
And Allah knows best.