Technology has always fascinated me - not just the tech itself but how it's adopted its' the social impact, which are not always foreseen or foreseeable.
I ran across a story of a clever Tesla driver who found a way to move his car between two hour parking spots to avoid a ticket by using the "Summon" feature, all without leaving his office. Neat but defeating the point of why a two hour parking restriction exists.
Today human drivers can drive around the block when they don't have a place to park and wait. For example, if they are waiting for a spouse who will be out shortly. Generally the price for doing so is free (a small price is paid for gas/depreciation) and what prevents people from doing so for hours on end instead of paying for very expensive downtown parking is that driving in circles in downtown traffic is not something that any human driver would want to do for any extended period of time.
Self-driving cars, though, don't have the same constraints. In some ways this will be a great thing - in future, cars will be able to drive someone to work then drive out to a free parking lot outside downtown (free parking forever!). Moving cars out of downtown will free up space downtown for better more human uses.
It should not be too hard to see the problems with this though - whether it's the story of the Tesla driver above or whether it's a car driving around the block for hours because the owner doesn't know exactly when he or she will be done with an appointment (and wants the car to 'stay nearby'). The increase in traffic if every commute required a trip downtown to drop someone off and another trip out of downtown to find a parking spot could double the time on the road. Traffic volumes downtown could increase rapidly to the point of total gridlock with self-driving cars that don't particularly hate being stuck in traffic like a human very much does.
Fortunately, the solution seems (to me at least) to be apparent: some form of tolls (which could even be targeted only at self-driving cars) would drastically reduce the number cars that would simply drive around, and would make car sharing services (that could more efficiently match people going in and out of downtown) would likely be the result. Of course, coming up with these incentives and getting the details right might be far more difficult that I'd expect it should.
One item in the law that will need to change though: with a self-driving electric car what will it mean to be "stopped" versus "parked" in traffic and how would a poor traffic cop be able to tell the difference?