No that’s not what it basically is, that’s the more recent religious reasoning added on top of what was basically a millenniums old cultural adaptation to the local climate.
If you look at how the men dressed in those climates, they’re also in voluminous ankle length long sleeve dresses with their hair covered and the hair coverings can be brought round to cover the face to protect against sun, sand blowing in the wind.
It’s we northerners that view covering the face as antisocial and we associate it with criminal activity. We put the negative spin on it.
The Imams have added a religious justification of modesty for men and women because as these ethnic groups migrated north, they obviously want to preserve their cultural identity even when it makes no sense to wear what is desert clothing in Glasgow.
https://deenin.com/en-gb/blogs/all-blogs/islamic-clothing-for-men?view=blogtestv2
The Quran emphasizes the importance of dressing in a way that is respectful, humble, and free from extravagance. This means wearing clothes that are loose-fitting, clean, and cover the body appropriately, ensuring that the focus remains on one’s character and actions rather than physical appearance.
Applies to men and women, masculine and feminine versions of that of course.
The English did the same in all the colonies- wearing full Georgian or Victorian dress from cold UK while in India, Egypt, Ethiopia, etc. Also for modesty reasons.