There are two obvious ways of fixing that situation. The first, recognize that trying to reach a location by individual cars cannot work out and ban private cars. Many European Cities have large pedestrian zones where private cars are locked out of whole streets in city centers.
The other option would be, and fortunately self driving cars would be part of the solution, to create enough parking spaces. Parking in the streets would still be disallowed, creating large pickup areas instead. So the road sides would be free of parking cars, enabling drivers to stop at any desired spot. As soon as the passengers left the car, the car would leave immediately for a nearby garage. This would of course depend on the creation of the necessary amount of parking garages.