I’ve had about 5 bike fits done over the past 7 years. Obviously when I’ve changed to a new bike, a new fit was required. As I got fitter and started racing, fits were done to improve/optimize performance matched to the needs of the type of racing, etc.
And all along the way, I’ve been a loyal Look pedal user. Recently, I’ve noticed that I wear through my Look Carbon Blades pretty quickly as a result of clipping in/out predominantly with my left leg. The wear on the pedal loosens its grip on the cleat over time. Not crazy like, but enough that i have found keeping my cleats on the newer side was helpful. After speaking with a couple of friends, i decided to try a set of Shimano road pedals. At the same time, I recently bought a new set of shoes - Sworks Sub6s (I’m a laces fan). In setting up the new cleats on the new shoes and hopping on the new pedals, I knew that pedal and cleat stack height, shoe sole thickness, etc all would be at play and I figured that I could use a second set of eyes to potentially make some adjustments. My last bike fit was from 1 year ago, and it was very thorough. I’ve enjoyed this fit and had zero problems with pain, even across massive long days in the saddle (i did a 7day LeJoG last season).
I have been using a Quarq DZero for over a year. In hundreds of rides, I have seen little to no variation in my left/right power balance. I’ve been 47/53 in 99% of my rides. It’s super consistent.
So yesterday morning I get my new fit done with a different fitter (acknowledgement here for fitters being different due philosophy, science/art variations, etc), and it’s a guy I work with and trust that he’s well experienced and knowledgeable. (I work part-time as a mechanic at a shop here in Germany). End result included some cleat adjustments, some saddle height changes - nothing major. However, looking at my Taylor -2 and Pettit workouts from the last 24hrs…my L/R is now 50/50. On both workouts. 
I’m intrigued. This was by no means a goal of the fit. It just happened. And I find this quite interesting (not shocking) that a change of shoes and pedals, with an adjustment made to saddle position = a shift in L/R balance from 47/53 to 50/50.
Bottom line - go get a bike fit done. Try different fitters, take details and nuances with a grain of salt, but trust in those that do this melting pot of science/art. I have a honours degree in biomechanics and I’m a certified bike mechanic and as much as I would love to just do my own fitting for myself, a second opinion is always worthwhile.
Thanks for reading!