Some of them will. I suspect it will depend on the tier you choose when you subscribe to the service. Lower tiers will be utilitarian, but you'll have the option to spend more to get a nicer ride.
Kind of like now - you can take the bus, or a cab, or a limo.
Routine "driving" won't be fun anymore, but then I can imagine a rancher in 1908 bemoaning the idea that he won't be able to play on his horse anymore too. I suspect cars are going to be somewhat like horses. We still have horses around. We use them almost exclusively for enjoyment rather than necessary work. No one rides a horse to work anymore. In 50 years no one will drive a car to work anymore either, but cars will still be around as hobby items.
I would guess the speeds would be very much higher than that. Most cars today could comfortably do 100+ if they had proper maintenance and a competent driver, and the guarantee that all the drivers around them are competent. Well, all that's gonna get solved by automating driving, especially when, as you correctly speculate, all cars are going to be part of a communication network so there won't be any surprises at all. Wouldn't surprise me to see 120mph and more on highways.
The disadvantage to buses is that they only come every so often, and they only go to certain places. That's not such a big deal in places like Chicago where those places are every block, and they come every few minutes.
Here in the Minneapolis area, if I want to go from my outer-ring suburb to the next outer-ring suburb over, I have to take a bus into downtown Minneapolis, then transfer to another bus that goes to the other suburb. I have to spend more than an hour going 35 miles in order to go a net distance of 4 miles, and if I want to make the trip at any time other than rush hour, I can expect to be waiting for each bus for a good while to boot.
And then the bus might stop 6 blocks away from where I really want to go. I'm not anti-exercise, but 6 blocks on a -20 degree February day, or a June severe thunderstorm is pushing my limits.
That's stupid, and no one in his right mind who can afford a car is going to put up with that. The nice thing about auto-pod-cars is that they will drive to you, when you want them, and they will take you exactly where you want to go rather than 6 blocks away.