My take on the harp is this:
The treble strings are necessarily shorter than the bass strings.
You've got to have the short side close to you, otherwise you couldn't reach all the strings.
Righties naturally reach out with their left hand, keeping their dominant hand closer to the body.
Melody is typically played on the higher strings.
Thus by default, not by design, the right hand plays the melody. A lefty could, and I suspect would, reverse this.