Kim, many of us have felt that the "off" hand has a harder job to do, at least in the beginning stages of learning an instrument. I even had a guitar store clerk suggest that I, a lefty, get a right-handed guitar for that reason (I'm sure the fact that his store had NO lefty guitars had no bearing on his advice, right?). That raised the question in my mind, then why don't music shops stock mostly or all left-handed guitars for the benefit of their right-handed customers?

And therein lies the "proof of the pudding"--pick up a left-handed guitar (or fiddle, if you can find one) and see how it feels. There's a great awkwardness to having your dominant hand farther away than your off hand--compare the standard positions used in boxing or shooting a rifle. For those with a strong sense of their "handedness", a "wrong"-handed guitar will never feel right.

I also gather that those who become proficient on their instruments (which leaves me out) use their dominant hand to do some really challenging and skillful motions in their picking & bowing, to where the off hand doesn't necessarily have the harder job.

So you're right, for most of us "it don't work that way", though there have been times that wish it did.