A cul-de-sac gets far, far less than double the traffic of a normal road, and vastly less traffic in the form of heavy vehicles. Road damage is proportional to the 4th power of axle load (according to the US GAO).
Weather-induced (largely water-induced) damage is driven largely by access to water provided by surface damage, which is driven by road weight and traffic volume similar to deeper damage, but also by traffic speed and resulting tire hydraulic action more than deeper damage is. Low-speed, low-traffic-volume roads than generally see personal passenger vehicles and smaller delivery vehicles without many heavy trucks will also see a lot less weather damage.