I do balance training, and anything involving standing on one leg (like juggling while alternating one-legged stands on a foam roller) I always start on the leg that wasn't the one I FELT like starting with, then religiously alternate so I do the same amount of time on each leg. But that doesn't actually mean I'm universally good about bilateral symmetry.
I've had a lot of right knee pain this year (even more than the last 7) and physical therapy pointed out some pretty substantial differences in strength between hips/glutes (weak) hamstrings (OK) and quads (insane) and in flexibility between the right and left side leg/hip/glute/hamstring/iliotibial/piriformis. (Various injury stuff, probably compounded by laziness in stretching only the randomly messed up side after various prior physical therapies. Although the main pain problem, actually, was being a bonehead: After my right knee started hurting a lot after exercises deeply bending it, I brilliantly decided not to make it "worse" by doing my standard quad stretch that requires acute bending of the right knee. Once I stopped stretching it, the quad tightness made the pain ratchet way up, which kept me from stretching it, and...)
So now, after 8 weeks of physical therapy, I've started working with a personal trainer* and am getting assistance in stretching out after each session. And my trainer is trying to keep me from doing 1-legged exercises with a greater range of motion on my "good" side, specifically to keep me from creating new strength and range of motion imbalances. It's been educational. And I'm acutely aware of how I baby my hurt knee side if I don't pay complete attention to that. More later about my uneven turns I figured out a couple of seasons ago.
*Official embarassing eating crow footnote. I always looked over at those working with personal trainers in the gym with a certain smugness, as I clanked another weight onto the bar above the squat rack. They were playing around, or doing little weight loss/body image foo-foo lifts. I was training seriously to get in shape for ski racing, which I knew a lot about.
What I was doing, is concentrating on the stuff I was already good at, or cheating by involving my back muscles in lifts I shouldn't, or piling on too much weight and having my form suffer. (Walking lunges are great, but if you pile on too much weight and your hips go funky, the knee doesn't track, and that pain is a byproduct.)
Spending an hour in supersets intermittently redlined just on the edge of the dry heaves, mostly concentrating on exercises or variants I've avoided, with a trainer who won't let me cheat, while discovering just how far behind I really am in my anaerobic threshhold training has been a somewhat humbling experience. I may still bump my head on the bar from time to time, but now it's more likely fatigue than a swollen head...