Yes, increasing availability of cars through self-driving will result in more trips, probably from underage or elderly people. But add in a service like Lyft, and the facts change. Taxi services reduce the total amount of miles driven.
When I first heard that it sounded crazy, but think of this scenario: you live near your friends, but go to work at different places. You all agree to meet up for a beer after work. If everyone takes the same taxi home from the pub, you've saved two car trips.
I'm not sure you grasp just how fundamental a change in our lifestyles a switch to driverless cars could be, especially ones sold on a subscription basis with unlimited usage. It's the difference between first world countries with socialized medicine and those without.
Before, driving was a job that everyone had and took up valuable cycles away from living your life. You had to consider each trip, e.g., "How much gas do I have? What's the traffic like? My car isn't working, I have to skip going out tonight."
After, no matter what you want to do, you just call a car and get in. You don't even have to think about it. It's going to liberate so many people that undoubtedly frivolous trips are going to stack, similar to how people in countries with socialized medicine tend to visit the emergency room for less and less serious medical problems.
Since Uber has come to town I catch myself calling it for things I could have easily skipped or taken the bus to or suffered on my motorcycle for (rain, etc.). I might haven taken, on average, less than one taxi per year but now take at least 15 Uber trips during that same time period. I think this sort of liberating convenience will only increase once driverless cars become popular.
When I first heard that it sounded crazy, but think of this scenario: you live near your friends, but go to work at different places. You all agree to meet up for a beer after work. If everyone takes the same taxi home from the pub, you've saved two car trips.