How would self-driving detract from fossil fuels? It should increase total demand for fuel.
In other words, people wouldn't need a big honkin' SUV or truck most of the time, and could ride around in something smaller with just the fuel range they need for that trip.
Also, traffic might get better. If everything became automated it might even be possible to eliminate traffic lights.
Traffic lights are also unlikely to disappear, as self driving cars do not magically get perfect traction or stopping abilities, and they will have to share the road with the other humans that exist on our streets, whether they be pedestrians, bikers, joggers, skateboarders, etc.
In contrast, a light rail alignment can move 20k people an hour. It also won't reduce traffic, but it'll slow traffic growth by reducing latent transport demand and allow cities to remain economically viable as traffic increases.
The average car spend 98% of the time unused, sitting in a garage or a parking lot. That is a lot of money that the car companies will lose when this technology hits mainstream.
That is a lot of money that cities lose when this technology hits mainstream :)