Piano music is mostly written by right-handers for right-handers. I'm strongly left-hand dominant. For music that's intended to be easy to play, the primary voice is almost always on the right hand. Where the music wants the most dexterity, I have the least.
At the developed level where the composer doesn't give a damn about how easy it is for the musician to play, yes, both left and right-handers have to figure out how to realize the piece and would make use of their strengths to do so.
For instruments like guitar I think the case for reversing the handedness of the instrument is a bit stronger, since the hands serve very different roles there.
I don't think that's the actual reason, even for teaching music. The primary voice is in the right hand because the right hand is higher and so the waves it generates have higher energy at the same volume, making it the easiest voice to hear. I assume that in arrangements and pop music, the arranger naturally puts the melody on top and fills in as much harmony as they care to (which is usually not a lot unless you pay for the arrangement).
> Piano music is mostly written by right-handers for right-handers
Even if that does not directly say that people (right-handers, specifically) insert their handedness bias into the things they write, it does certainly imply that that is important for people who write piano music to put the athletic part (the melody) in the more dextrous hand. It is not. The reason for the right hand to carry the melody is the sound projection of high notes, nothing to do with handedness.
Incidentally, many famous composers in the piano canon were lefties. Rachmaninov, Prokofiev, and Ravel all have strong evidence of being left-handed. CPE Bach may have also been a lefty, as may have Mozart and Beethoven. This is not "right-handed people making right-handed music" by any means.
At the developed level where the composer doesn't give a damn about how easy it is for the musician to play, yes, both left and right-handers have to figure out how to realize the piece and would make use of their strengths to do so.
For instruments like guitar I think the case for reversing the handedness of the instrument is a bit stronger, since the hands serve very different roles there.