I thought this was a thread on car ownership, not car use.
If you hire a car, you can choose an appropriate vehicle for your needs. If it's a single person commuting 10 minutes at 4AM, perhaps a small electric car would be perfect for your needs. If you're going on a 600 mile holiday to scotland with a lot of luggage, perhaps a roomy estate with a large tank would be a better choice. The cost of a car journey reflects the entire cost, there's no sunk cost.
When you own a car, you have to make a decision on the type of car based on all your travel needs - both popping to the local haberdashery, and driving 4 hours to visit friends for a weekend. You have a sunk cost of £x per year, which you have to pay regardless of how much you use it, this makes the marginal cost cheaper, but the overall cost higher than it needs to be.
So on reflection for many people hiring makes perfect sense. And once that is in place, for many trips public transport becomes viable for some or all of the trip. The problem then comes in the overhead of hiring -- getting to the hire place, filling in the paperwork, short term hiring being impractical for the majority of cases, and if you only need the car for 2 10 minute trips a day why would you want to park it at work and hire it for 10 hours?
Carshares reduce the overhead by putting the cars near to where you need them (like Boris bikes) but only work in dense cities, and can't be relied on due to the limited numbers in a given space, and the flow of traffic into work areas in the morning and out of work areas in the evening.
Robots that deliver a car within 5 minutes (where it was parked on non-valuable land, recharging batteries, or was returning from a previous trip from housing->industrial) however change the dynamics by reducing the overhead of hiring a car. If the fleet is large enough there's no need for many people to have the hassle of owning a car, as there's always one on tap, order just before you put your shoes on, job done.
Taxis do this to some extent, although are more expensive per mile than a hire car due to the cost of the driver. One other thing that does stop me using a taxi more is the car seat problem - when you have kids, you need car seats. When you own your own car, they are always available. When you get a train somewhere, and want to get around an area, taxis go out of the window
If you wanted to discourage car ownership, one way to force appropriate use of resources would be to ban on-road parking between the hours of 3AM and 4AM. If you want to own a car, you must have somewhere to store it. It's really unacceptable for people to take ownership of 6 square metres of public space on a constant basis. At the very least the ban on driving on the pavement (unless accessing private land) should be enforced.
If only 10% of drivers moved to public transport, the system would collapse (rail usage would double for instance), so any change in peoples habits need to be gradual.