Statistically, assault by Uber drivers is really rare, but enough people take enough rides that I know multiple people who have had these experiences. Uber needs to have super-strict privacy controls and auditing on this, but it'll make a lot of people, especially women, feel more comfortable with taking Ubers.
As for privacy, you have no reasonable expectation of privacy in a public place. An Uber car isn't any more private in theory than a train or subway. If you want privacy, stay at home or get your own car. Uber already knows where you're going if you use their service, so this only gives them access to any conversations you might have. Simple: keep your mouth shut in the car. Why would you have a super-private conversation in a cab anyway, with some stranger who's driving you right there?
https://ecollections.law.fiu.edu/cgi/viewcontent.cgi?article...
Truly the best solution to privacy erosion.