The main promise of autonomous, self-driving vehicles is an increase in road safety. We lowly humans are prone to distraction, emotional/erratic behavior and drunkeness - none of which typically afflict the computer systems being tasked with controlling our vehicles.
A look at current and recent automobiles reveals quite a bit of "driving assistance", in the form of crash avoidance, lane change warnings and so on. Quite a few vehicles will already allow "hands free" driving under some circumstances - Tesla's "autopilot" being a well-known example.
Even though these additions should tend to make things safer, the real promise may not show itself until the vast majority of vehicles are "fully autonomous" (level 4 or 5), as defined by the NHTSA in October 2016.
Currently, most available automated systems are level 1 or 2 with some level 3, and it may be that some drivers over estimate the abilities of some of these current system - as possibly seen in the recent tragic Tesla autopilot accident (the driver may have been watching a movie when the vehicle struck a semi).
Only at level 4 autonomy is a human driver theoretically "not needed" to drive from A to B, but even then that is under what might be considered "normal" driving conditions, on regular roads.
Ultimately, level 5 systems would be expected to be able to drive autonomously on dirt roads (for example) and in adverse conditions where an experienced human driver might typically be expected to operate.