Most of the reason for that (at least in my experience) isn't about some deep desire for privacy, but for the prosaic reason that it's a nuisance to arrange wit

Most of the reason for that (at least in my experience) isn't about some deep desire for privacy, but for the prosaic reason that it's a nuisance to arrange with someone else to meet at a certain time and place, to make sure that everyone in the car pool gets out of the house in the right 10 minute window, etc Being able to just call a car to drive you to work, while an automatic system figures out the car sharing arrangements in real time, could remove a lot of the barriers.