Personally, I think it's a good idea and I wonder why they didn't do it long ago.

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?