Who is going to use these cars when everyone is in school or at work or sleeping. This will not solve any issues since most people follow the same schedule.
Transportation demand would still be "lumpy", but surge pricing would encourage people to shift their transportation needs to save money. Deliveries would probably be one of the common uses during the workday. Utilization would not be 100%, but it's certain to be more than the 0% productive use that parked cars currently have.