This article is not the defining answer to the question, just one's attempt to shed some light on the subject.
The author interviewed a number of experienced archers and received a variety of reasons "why" they selected right or left wing feathers. Most of the reasons are represented here so we find that little has changed over the years.
IMO, the findings support just about all of our preferences. By that I mean "right or left" doesn't make a noticeable difference in accuracy at the ranges we need it.
I use right wing and have no idea "why" I initially started using them, but continue to do so, mostly from habit, but they do what I need of them and are easier for me to fletch.
There is nothing in my experience that suggest I would improve my accuracy with a change. They are other variables requiring improvement before I would even be at the stage I might could notice a difference.