Well, car needs roads and roads are public goods. And, of course, they need a lot of public funding, planning and maintenance. All with public money.
Governments pushed for cars as a mean of transportation because in the Keynesian era was good for the whole economy (car factories employed a lot of people), and nature was less of a concern. But pushing for cars was a deliberate public policy that involved a lot of public infrastructure, city planning, etc...
Driverless cars would need a lot of infrastructure as well, but I don't think they are a good investment for the whole economy like normal cars were in the '50s. With putting a lot of public money for infrastructure to help a few companies that do not employ so many people anymore?
The future is not for cars, IMHO. But who knows...
Self-driving pickup of my groceries? Check. Self-driving pickup of my dry cleaning? Check. Self-drive me overnight to next vacation? Double check.
The future is bright, and it's chock-fucking-full of (self-driving) cars.