"Right and left handed people alike customarily play the violin right handed. Violin teachers instruct all of their students to play right handed whether or not they are naturally right handed."

That's just not the case. Not saying that M.O.H. is wrong. He just quoted an article that clearly got it wrong. Could be that some orchestras only hire right handed fiddlers but there are plenty of left handed violinists around who play left handed. Ashley Macisaac comes to mind but there are plenty more.
I seriously doubt that there are many musicians capable of playing such an instrument with their non dominant hand. The fine motor skills required not just to play but to adorn the music, just aren't there.
It would certainly awaken the artistic side of the brain but the concentration required would seriously conflict.