5. Right, left, right, left . . . Why don't we use the dominant side of the body? It may cut the training time in half!

... Yes, but you are just half way right. The total equation is completed when bilateral motion of the body is strongly emphasized in martial arts training. The student is discouraged from favoring his dominant side, so that equal proficiency in skills on both the left and right sides is developed. Extra attention is devoted to the weaker side, with more repetitions, resistance, or time spent working that side.
... Although it is best to learn a technique on the more proficient side, when practicing one should begin and end on the other, weaker side. This is important not only to avoid displaying a weakness to an opponent, but also to maintain a balance in the strength of muscles across the pelvis, back, and shoulders that help control the alignment of the spine. We may appear to be straight on the frontal plane, and have natural curves on the lateral, but a top view might indicate a twist in the relaxed position of the pelvis or shoulders. This can inhibit flexibility, or lead to a shearing effect of the vertebrae under a load or unusual stress.
... From a self-defense point of view we also have to consider the situation where an injury might prevent us from using our "better" side. Also, it is scientifically proved that practicing on the less skillful side will improve the better one directly. Think about it . . . with both sides of the brain of course. Take care.