“And this Psak from the Mechaber plays a direct part for the shittas that rule that women aren’t permitted to drive.”
As per Rav B Zilber, it is the other way around. The above is only another reason for them to indeed drive. As they will not have to walk on the streets and travel by bus or by a male Taxi driver.
The fact of reality is women are on the streets of BB, Jerusalem etc.