When a roller rolls on a flat surface at constant speed without slipping, static friction is present but does no work, resulting in zero net friction force. If the roller maintains constant velocity, it implies no acceleration, meaning friction does not affect its motion. The discussion highlights that while static friction exists, it does not influence the speed of the roller under these conditions. Any discrepancies arise only when considering forces that would cause acceleration. Overall, friction plays a minimal role in this scenario, primarily coming into effect only during changes in motion.