Cars being parked idle all day isn't necessarily going to be a bad thing, most Vehicles self driving out there are EV's and even if it's a standard combustion, those have migrated over to an engine off when stopped ideology where it just doesn't run until someone presses the gas. It wouldn't be infeasible for the company's developing the technology to have an electronic climate control system that just auto-offs when there isn't a passenger in the seat, a sensor that would be a hard requirement for a self-driving vehicle anyway. Which means that it's very likely that the vehicle could even if it was a combustion engine be idle for extended period of time without it taking up too much more resources.

That being said I do believe that electric vehicles would be the optimal vehicle for this, as the only thing it would need to do when it didn't have an order would be have the radio transmitter on which shouldn't take all that much electricity which means it shouldn't drain the battery and furthermore there could be designated charging stations that the car can idle at near these population hotspots like described.

You have to remember as well that once Society transitions to a system that's like that, there is going to be people that don't bother having vehicles themselves so I believe that there's going to be more space freed than space used by doing this change