I think this is too optimistic. Self-driving cars only work because they are in the minority. Can you imagine a city full of current state-of-the-art self driving cars and it not turning into a traffic chaos?
In particular, I think that self-driving cars cannot work fully autonomously without communicating with other cars or the road infrastructure. And I am not aware of any effort to create a cross-vendor car-to-car communication protocol.
There are trivial cases where pure autonomous following of traffic rules will lead to deadlock (or other issues). Take these two simple examples: 1) 4 cars arrive at the same time in a four-way intersection without signals or yields 2) on a three lane road, two cars from the outer lanes try to switch to the middle lane at the same time.
These are by no means difficult problems (I'm sure there are more difficult cases too), but they must be solved and so far they're not being worked on.
Sometimes the communication needs to be complex (I.e. Verbal). I've had a few instances when I've had to negotiate to unblock a traffic deadlock, mostly when a two way lane is constricted to one vehicle only due to parked cars, or a HGV which is too big to drive past. In London this happens quite frequently.
I really cannot think how an autonomous car, with no human inside, could handle these scenarios.
And driving in non-inclement weather. And driving in places that aren't meticulously mapped by Google. And being able to refuel themselves....
I'm not denying the accomplishments of current autonomous vehicles, but there is still a ways to go technically.
Designing for the unexpected edge cases is harder than designing for the normal cases. In accordance with Cargill's ninety-ninety rule, we can expect that the "fine tuning" you mention will be turn out to be a very big job.
As an extreme demonstration, consider the fact that you could rack up a million "autonomous" miles in a matter of months, using vehicles capable of nothing more than "lane keeping assist" and "adaptive cruise control" - just set 'em loose on a NASCAR loop and run them around in circles until this artificial example's point has been proven.
I am exited about autonomous cars, but I'm not convinced they are as ready as various companies want us to believe.