Not really. Accidents are a function of driver and environment. You can't control the other drivers. If you think of the primary purpose of insurance as to make sure that the party not at fault is made whole, then perfectly priced insurance becomes like posting a bond in order to drive. Which isn't unreasonable.
(Plus uninsured motorist coverage for the other parts you can't control, which really is an insurance function.)
Maybe it would be lower relative to other people's rates, but one must imagine that any insurance prices will only ever cost more to the consumer.