“There’s still the issue of the tznius woman being an eyesore”
That’s not a halachic reason, and since you didn’t provide any source I’ll assume it’s because you can’t because there are none. Unlike the more left-wing posters, I would be willing to hear you out were you to provide any real evidence. Also, unlike them, I am not belittling this minhag or claiming you’re making it up. However, claiming that lo tisgodedu applies here seems to be made up by you.
On a side note, Ezras Nashim for sure operates in Williamsberg. I thought they even originated there. Their Satmar volunteers do not drive.