Yes, that "elbow flare" (prevention) is another good point.

And to be specific, if you turn you hand anytime before the END of the punch then the elbow will necessarily flare out, turning it once the arm is practically straight (i.e., right at the end) will not matter.

So if you want to hit with a horizontal fist for any reason, including the 'shoulder position' being a better defensive posture then you must wait to turn it.