When I fought Muay Thai I had over a 1" height discrepancy between my left and right hips due to the increased muscle tone from rear leg round kicks. With some dedicated stretching and working equal amounts on both sides this is no longer an issue.
I do not know if working both sides would benefit things like boxing, kickboxing. Few seem to do this type of training at higher levels. Grappling it seems lends itself to this type of training better.