I know a bit about this topic because I did a business plan on it for my final term group project last year.
Personally I don't like it one bit as I it is completely sexist. Thankfully, such businesses would be breaking anti-discrimination laws of the EU. There are organisations who are offering such services via a "loophole", by going not for profit, such as Pink Ladies in Warrington with over 7000 members iirc and other companies in Manchester and London.
Our team were able to come up with a way of appealing to the same target market without being discriminatory. We were allowing members, i.e. those who would provide their details, the choice of drivers. So if they had any qualms, they could choose the driver who, from our side, just happened to be female. Although selecting a driver by sex/gender is a practice that we neither encouraged or discouraged, we advertised the ability to choose the driver in general as a USP amongst the other safety features we provided.
The same features should help attract female drivers, but we would also station specific drivers to membership-only customers.