In summary, what both studies demonstrated was the power of the bilateral deficit. The research is representative of what we often see in that gym in that unilateral strength and power training can improve both unilateral and bilateral strength and power measures but it does not work the other way around. Structurally and neurologically we are unilaterally dominant creatures, designed to move in contralateral patterns with one limb at a time. By choosing training methods that are congruent with how our bodies are designed not only is it more effective but it also appears more efficient.
Numerous studies, including the second one I referenced have found that we are able to achieve increased ground reaction forces and higher velocities with the same same external load per leg unilaterally as we can with bilaterally. This means higher motor unit recruitment and velocity of movement with less total load on the nervous system and spine.
This may be especially important for athletes training with a history of back pain as they can pursue a training effect in the lower body without increasing training load on the spine.