Autonomous cars are generating considerable buzz for many reasons, but one of the most dramatic centers on public health: Many say self-driving vehicles could drastically reduce—or even eliminate—the tens of thousands of traffic fatalities that occur annually in the U.S.

Human error plays a role in 94% of all traffic accidents, according to the National Highway Traffic Safety Administration, which is why auto makers and regulators believe self-driving vehicles have the potential to be so transformative. Once driverless cars...