The only reason not to play with the elbow too far to the right is the bad angle that your fingers can have on the E string. The angle is slightly different for each string but I prefer to move as little as possible when playing fast. Also it is possible to adjust the wrist as long as you only make slight adjustments. Some people don't have fingers that are flexible enough to play the first 5 positions on the E string without keeping the arm further to the left. The problem is that if you go high enough up in positions you will have to move your arm over anyway to get around the fingerboard.

I've had professional musicians take just a few lessons with me and make radical improvements with only adjusting the basics. You, Oliver, are a smart man who sees the logic of simple and obvious solutions.