Even assuming everyone commutes at the same time, the status quo cars sitting idle the rest of the day, the only difference is that they need two or three spaces to park each, and typically in high value locations. Your car sits at home at night and at work during the day. With the car service there could be half as many parking spaces or less, and they can drive themselves to a garage in some remote area, rather than within walking distance of a place you want to be.

The car service makes car pooling and mass transit more practical as well. Maybe you could hitch a ride with someone to work, but then you might have to stay late. With personal car ownership, you need to drive alone both ways, but with the car service, you can share the morning trip and if you need to take separate transportation in the evening. If buses in your area can't reliably get to work on time, you could have the car service pick you up to go to work, the the bus take you home.