If Uber and Lyft are reliable and affordable, then you do not need to own a car.
He does, to his credit, say "if", but the reliable and affordable are never going to be affordable enough. Kling's view of the economy is summed up by his description of Patterns of Sustainable Specialization and Trade (PSST), whereby complex relationships are constantly trying to find an equilibrium, he would be good to think of the complex relationships Americans (in particular) have with their cars, and how that could be replicated in the real world.
First off lots of people customize their cars, and I am not talking about rims and paint jobs. One of our cars has two kids seats in it, with straps adjusted to their sizes, a collapsable stroller in the trunk along with a fair amount of dirt, bits of snacks wedged into the seats, and various toys and children's books scattered about. For a ride sharing company to meet my individual demand for a car they are going to need at the ready a car with two kids seats of the right size near my house, not have a passenger shortly after me allergic to peanuts, and not care or charge for cleaning out dog hair, mulch or topsoil. I may be unusual in the specific things that I do with my car, but I am hardly unusual in that I do specific things with my car.
The second problem is one of use patterns. The issue with rentals of any kind is that there is always a peak load that needs to be filled. Hotels are expensive not because it costs $36,500 ($100 a night) a year to build, rent, maintain and profit off a single hotel room but because most nights hotel rooms sit empty, and then a handful of times a year they are packed to the brim. It is a fact of life that the times that you want to use X are usually the times lots of other people want to use X. For the majority of people to use Uber or Lyft instead of their own cars their fleets will have to be large enough to accommodate the peak load on roads, you know, rush hour. Not only will they have to be big enough to handle the average load, but they will also need to be big enough to handle the worst traffic days when an accident, breakdown or construction doubles commute times, and all the 9 am traffic who, theoretically, would be riding around in cars that the 8 am traffic used is suddenly stranded and running an hour late.
Lastly fully automated autos are going to reduce a lot of the non financial costs of driving. The boredom of sitting in traffic will be replaced by entertainment, the discomfort many feel sitting in car seats can be replaced with better designs now that the steering wheel is out of the way, and the safety risks of driving should be mitigated. An economist should expected that self driving cars will reduce the costs of driving, and so should increase the incidence of driving. This should mean people get more use and value out of owning their individual car(s), which will push back heavily against corporate ownership.