I apologize for not being clear enough, I'm not saying there should be left handed weapons or animations. I'm saying there should be an option to bring your weapon to your left shoulder while maintaining a right handed pose. In other words, your right hand stays on the grip while the gun is on your left shoulder.

The purpose of this suggestion is simple. It exposes less of your body in certain situations. Since your gun is on your right shoulder, you are able to shoot from a right sided corner without exposing too much of your body (without leaning). Now if you were to shoot from a left sided corner, you would have to expose more of your body since your gun is shouldered to the right.