Yes! The far suburbs of Nashville aren't going to see UberTeslaWaymo fleet cars; the utilization would be far too low. They'll see what they see right now: one or two drivers on Uber or Lyft. And the trip price will be higher to reflect the human driving the car.
Well, with respect to the topic of this thread, those are specifically the jobs which people might purchase the car and sub it out to a company for a shared profit. If the cars are autonomous, there's no need for the driver to be there. It could become the equivalent of a paper route, and extra way to make some cash on the side during what are traditionally non-work hours (in this case, the cleaning and mechanical upkeep of the car).
Cars deprecate by mile as much as by year (ignoring the initial drop which is only based on a non-zero preowner count instead of time or distance). So unlike a driver, who is as expensive while driving as while waiting, a robocab spending much of its time on cold standby would not require a terribly high premium on trip prices.
Adoption in the suburbs will still be much slower, but mostly because unused car storage is so much less of a headache out there.