No no, I get it. First I thought you meant like a neighborhood thing where they share a car among a few houses, but this faces some of the same problems. Mainly that your need for a car isn't the same at every hour of the day. Much like roads that have to be built to handle the peaks in traffic, such a service would have to do the same. You need a car to go to work and to come back. At that point if you wanna offer a service comparable to actually owning the car (wait time close to 0 and the most efficient route, i.e. no car pooling) you are talking of almost having a 1:1 ratio of cars to people.
At that point it seems better to just own the car. Plus how much do you pay? Per use, per miles used, everyone pays the same? You'd still be better off owning the car. In fact it would be much better to own a car the drives itself versus the car you have now, since you could have it go park at cheaper locations (and it would drop you off right at the door of your work).
I don't really see the value in a service like this to be honest.