I think drivers in this category should be entitled to reduced premiums. As a matter of fact, careful drivers who stay accident-free DO get rate reductions.
Most companies offer reductions for five years claims-free driving.
Some companies may reward accident-free drivers for six or even seven years. The premium reduction could mean that you are paying only half the rate that someone with the same car who has had an accident in the most recent year is paying. However, there is a wide variation in companies' rules in this area. Ask your insurance provider what your insurer would charge if you have a claim. You should also know that some companies do not automatically increase your premium if you have a claim after a long period of claims-free driving.