One-sided running allows you to focus on one component on either the left or the right side. For example, you could think of pulling with the right glutes in the top speed phase. Focusing on only one side gives you time to complete the full range of motion. In contrast, thinking of both sides can get confusing as you run. This seems to lead to shortening the range of motion. When thinking of both sides, you switch from thinking of the left side to thinking of the right side. I think that the time it takes to switch your focus is time that is taken away from the final range of the desired motion. With a one-sided focus however, I have found that while focusing on the full range of motion on one side, it forces the other side to balance out the motion and complete its full range as well.
To try one-sided running, start with just one component. Practice for several weeks until it is automatic and then practice the same component on the other side. Go to another component, and continue through the major components. Then combine two components and repeat a similar progression. As more components become automatic, three or four can be combined to be one focus. For example, right glutes combined with left hamstring and hip flexor, and right arm pulling forward with left arm pulling back. This combination has one movement per limb, but by completing the full range of motion with each, the other side must also complete a full range of motion. This is all accomplished while having to only think about half of the total movements thus decreasing the mental time and effort required. By decreasing mental time and effort, the physical inefficiencies associated with thinking about them are also reduced.