If you own a car, the marginal cost of an additional trip is low (basically just gas). If you don't have a car, the cost of each trip will reflect its true cost. Basic economics will tell you this will lead to less trips, trip consolidation, other modes of transportation (walking/bike) chosen as primary transportation because ride sharing is there if you really need it. The really big cost that most people consider is parking. If large wasteful parking lots are eliminated, cities can become more compact which in turn will cause even more people to give up cars and so on.
As to your point about sharing, at some point if you want to be in the car by yourself it will cost extra. Again, economics...