Joseph,
I saw the Teshuva and there is no mention of anything to do with הלכה, Rav Wosner agrees you can NOT prohibit it in terms of any Halachik basis and, there is no proof or any source saying driving is any different than just walking on the street. (He agrees you can not bring proof from the times of the Talmud)
The rest as they will say, אין זה אלא דברי נביאות. And is not something that binds anyone to have to be machmir.
Yes, if the custom would have been that women limit their appearances on the street etc then it has a pshat. But as it is, walk down any street in Bnei Brak and it is full. Same with all other cities mentioned.
Hence, the concept of תקנה ומנהג has no effect there. As it all depends in the circumstances.
As far as Hilchos Minhogim is concerned nowadays, it has no effect of anything that falls into any category of either Minhag based on Halacha or סייג. it seems to be just a Chasidish based custom.
You have no other source than just the mere saying “that Rav Wosner says so”.
Rav Zilber and others have a very strong case why yes. They say rather they should not travel on buses along other men, or having to take taxis with men drivers. The fact is, women are much more active today, most women work and need to travel to get there.