Ignoring miles already driven, as you have, 6 billion miles = 3 million miles (5 million km) per day X 2,000 days (5.5 years). The number of miles is growing fast. If they double every year, the cars will be here in less than 3 years.
You failed to state your prediction of when we will have self driving cars, is it 3 years? Seem, like politics will take longer than engineering based on your numbers.