I think if I had a learned on a reversed piano - it would not transfer to a regular piano - I would be able to play better.
What which hand is responsible for (melody, accompaniment/rhythm) have very different dexterity requirements. Learning melody on the dominate hand would be preferable to me, in hindsight.
With an electronic keyboard, reversing the tones should be easy enough to do. However, I have not noticed that feature.
I suppose that it's easier to start out right handed on guitar, though, when the right hand is more active than the left hand.
Personally, fretting with my left hand just doesn't feel natural. When I first got interested in playing, I asked a salesman at a Guitar Center about left-handed instruments. He handed me a standard guitar, and showed me the fingering for a G chord. It was uncomfortable, but that's obviously expected for the first time I'd ever held a guitar. However, when I flipped it around and fretted with my right hand, it felt much more natural. So ever since, I've played left-handed.