You can clock up several years of no claims bonuses, and the discount increases with each year.
Interestingly, the no claims bonus can be insured. Now, generally only risk averse people will insure their no claims bonus - and these people also tend to drive more risk aversely and hence have less accidents (or perhaps less likely to make claims - who the hell knows).
So, the very fact that somebody wanted to insure their no claims bonus should in theory give them a discount on their premiums. But you cannot offer a discount for an extra feature! This means you have to dive into your generalized linear model and fiddle with a couple of parameters to make sure there is some sort of nominal charge for the insurance on the no claims bonus.
The whole point being that just because data is available does not mean I can use it even though it may be statistically significant for me to use it.
Again, I am not sure of insurance regulations so there may be a possibility around using more data, if available, in insurance models.
To your specific point, in my country we have the concept of a "no claim bonus" where the insurance premium is drastically lower if there is no claim made in a year - not sure whether there is a similar practice in the US.