Asymmetry seems to matter with pathology.

image credit: https://commons.wikimedia.org/wiki/File:PSM_V46_D167_Outer_surface_of_the_human_brain.jpg

When you have low back pain, your gait is apt to be asymmetrical

...And that is just what this study showed. It looked at 82 right leg dominant folks with slightly less than 1/2 of them havong low back pain. The folks with lower back pain spent more time on their non dominant leg at the beginning of a gait cycle and on their dominant leg at the end of it. Not surprising that they wanted to find a more stable base or center their COP over the weight bearing foot, especially in light to the fact that the back has such poor cortical representation.

Sung PS, Danial P. A Kinematic Symmetry Index of Gait Patterns Between Older Adults With and Without Low Back Pain. Spine (Phila Pa 1976). 2017 Dec 1;42(23):E1350-E1356. doi: 10.1097/BRS.0000000000002161.