Self Driving Cars: Would you ride in one?

Or would you buy one?  Long article in the Wall St Journal this Saturday about self driving cars, relations between Silicon Valley high tech and Detroit car makers.  Gist of article, Detroit ignored self driving cars until very recently, and now wants in. 
  Possibly, or perhaps not, the technology will mature to the point where the car's sensors (radar? TV cameras? lidar?) are good enough to detect the road, the shoulder, the center strip, and ignore the humongous radar returns from large signs, detect pedestrians, bicyclists, deer, objects fallen off trucks, and other cars all well enough to avoid collisions.  And can handle driving after dark, in the rain, and handle snow safely. Assume that the self driving car will not attempt passing on two lane roads.  Assume that the self driver keeps acceleration, steering and braking gentle enough to avoid panicking passengers.  And it has mastered things like parallel parking, and pulling up to the gas pumps without bending a fender.  All of these are stiff technical challenges that today's self driving car cannot meet, yet.
   But  assume they do perfect the self driving car.  Would you ride in one, in city traffic?  Would you feel comfortable riding in one?  Would you buy one with your own money, even if the self driving equipment were  fairly cheap?  I wouldn't.  I enjoy driving, been doing it for years, and feel best when I am at the wheel.  Even with one of my own grown children at the wheel, I get tense.  Eldest son is fairly good, but middle daughter and youngest son are down right scary.  Will I feel better about turning the wheel over to a microprocessor?
   I can see where the Ubers and Lyfts of the world would buy self driving cars.  If they work, don't scare the passengers, and don't get into many expensive traffic accidents,  they would eliminate paying drivers, which will do good things for the bottom line.  But  how many vehicles would Uber and Lyft buy, compared to the 10 million new cars sold each year to the general public in North America?  Enough to interest Ford or GM?
  Could it be cost effective for third party companies to sell and install self driving equipment in an otherwise standard car?  Or is it cheaper and easier to build the self driving equipment into the car on the production line?  I can remember when automobile air conditioning was just coming in.  You could get air conditioning installed by third parties, but every one agreed that "factory air" was better.  Will self driving equipment work out that way? Or not?