You're acting like one of those people who say that we don't have all the evidence on global climate change yet. There's no mystery about what causes motor vehicle collisions. Here is a huge report from the administration to Congress on the causes of motor vehicle collisions.
http://www-nrd.nhtsa.dot.gov/Pubs/811059.PDF
The majority of crashes occur in daytime, in clear weather, while the car is moving in a straight line. You'll note that substantially all of these causes would be solved by a computer-driven car.
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About 41 percent of the driver-related critical reasons were recognition errors that include inattention,
internal and external distractions, inadequate surveillance, etc. Of these, the most frequently
occurring critical reason was inadequate surveillance that refers to a situation in which a driver failed
to look, or looked but did not see, when it was essential to safely complete a vehicle maneuver. This
critical reason was assigned to drivers in about 20 percent of crashes. Internal distraction as a critical
reason was assigned to drivers in about 11 percent of the crashes.
About 34 percent of the driver-related critical reasons were decision errors that included too fast for
conditions (8.4%), too fast for curve (4.9%), false assumption of others’ actions (4.5%), illegal
maneuver (3.8%), and misjudgment of gap or others’ speed (3.2%). In about 10 percent of the
crashes, the critical reason was a performance error, such as overcompensation (4.9%), poor
directional control (4.7%), etc.
Among the nonperformance errors assigned as critical reasons to drivers in about 7 percent of the
crashes, sleep was the most common critical reason (3.2%). The effectiveness of vehicle-based
countermeasures used in mitigating the effects of various driver performance, recognition, and
decision errors could be evaluated using this information.
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You'll note that "vehicle problem" is the critical pre-crash event for only 1.2% of crashes. Therefore if the computer _only_ solves the sleeping driver problem, and even if it is twice as bad as humans at handling vehicle mechanical failure, society is still reaping a net benefit. But, of course, computer-driven cars can solve nearly all of these causes of crashes: inattention, misperception, distraction, sleeping, driving too fast for conditions, and on and on.