All depends on what you read as "significant improvement".

A 20% lower fatal crash rate compared to the average might be a significant improvement-- from a public health standpoint, this is huge if you could reduce traffic deaths by 20%.

But if you don't get the worst drivers to replace their driving with autonomous, that "20% less than average" might actually make things worse. That's my point. The bar has to be pretty dang high to be sure that you will actually make things better.