I see a couple of extremely powerful advantages to having a self driving car.

Your family only needs one car. You go to work at 8, and your kids go to school on the way so you drop them off. You get to work at 8:15, the car drops you off and heads back home. Your wife heads to work when the car gets back at 8:35, she gets there at 8:45. Your kids get off school at 3, but they have an after school activity so they let the car know it can charge up until 3:30, when it comes to pick them up. It drives there, picks the kids up at 3:45, gets back at 4, drives back to pick you up, brings you back home, drives to pick your SO up at 5, and by the time your SO gets home you have dinner ready.

If you're a single person you could probably split the car 5 ways with your friends. You could probably make a lot of money if you make an app that says "Pick me up here, my current GPS location, and drive me to work 15 minutes away at 8:00 AM every weekday. Bring me from work at 4:30 to a destination of my choosing after work". You could extremely accurately predict the price of transit, you know the probability of accidents. It's cheaper than any taxi, it's convenient.

Few accidents, no traffic jams, courteous to drivers, no speeding or parking tickets (unless you 'opt in' to speed), leisure, take a nap on the way to and from where you're going. The cars return to 'base' which is a parking lot that has a roof outfitted with solar energy, allowing the cars to store energy during the day. When cars weren't being used, if they still have juice, they either share the energy with the other cars that returned, or they compensate for the lack of renewable production at night. Some cars are 'regimented', where they follow the same pattern every day of the week. How much energy they use is known, they know how much energy they need to start the day with, and how much they can contribute back to the grid. There's other cars that are free runners that are always kept charged in case they need to drive to somewhere 4 hours away.

It'd be a little bit of an inconvenience to move things, but If you wanted to go from city A to city B, but needed to recharge halfway, you could just jump out and jump into another car at the charging station. NFC to verify who you are, grab your things and go. When you're driving towards the recharging station, it knows what music you have playing, what temperature everything is at, it preheats or precools the car for you - to ensure that swapping cars doesn't feel like swapping cars. Maybe you go to the bathroom at the rest stop, and when you come out the car is ready to go with all your belongings swapped. Put a little container in the middle that you can stash stuff in, just grab that when you change cars.

And carpooling - if you have 10 people that go to to work 15 minutes away, get some sort of carpool system going. First person gets on, the car drives to the next house, waits 2 minutes for the person to come, if they do great, if not they take off towards the next house. You say what time you want to be picked up, and a time within 10,20,30 minutes that you'd like to get there. Cheaper service if you have a bigger window of availability. Car texts you when it's outside (you can follow it on the map once it engages your current location).

I like thinking about electric cars.