“If someone had told you 10 years ago—even five years ago—that a major American car company would announce the mass production of a vehicle with no steering wheel, you would have said they were crazy.” With these words, Ford CEO Mark Fields hopes to wave regulators out of the way of fully self-driving cars.

Ford announced last week its fully autonomous cars will be on the road by 2021. This makes Ford the first traditional auto maker to join Google in focusing on cars that can’t be driven by humans. The combined influence...