A mora d’asra or community posek surely has the right and obligation to rule on halachas and hanhagos for his kehilla. Many of these communities are very large in their own right. And this particular hanhaga is very far from being only practiced in small groups. It his adhered to by large kehillas in America, Europe and especially in Eretz Yisroel. And surely relying on the Posek HaDor Hagaon Harav Vozner is a strong basis.
And it has already been explained how it certainly can be reasonably extrapolated from the S”A on Kol Kevuda (which is a tznius issue) as well as the woman wagon driver issue.