I am left handed and have been playing the violin and viola for over 20 years. I cannot honestly tell you that the left hand position and technique is easier for me to play it with my left hand because I have never played or tried it with my right hand. I know in order to do that I would have to relearn how to play the instrument left handed.
As for why it is only played this way, it is because if you play in an orchestra left handed, your bow will be going in the opposite direction from everyone else causing you to bump your bow with your stand partner because no one plays violin left handed.
In response to the person above who answered that all musical nuance comes from the bow…well it also comes must from the left hand. The violin has no frets like a guitar, so you must use your ear to adjust your left hand. Over time you do it almost instantly. That’s how fast the human ear reponse is. I don’t think a machine could do that. Also, you can do vibrato with your left hand, which adds to the musical nuance. Some pieces have sections that will even call for no vibrato, or fast vibrato or slow vibrato. Also, with experience you will learn when to use fast and slow vibrato with no markings in the music. This helps convey the feeling of the music. I doubt a machine can do that.