That brings use to the "cause" of the shift. As the left back/shoulder muscles are put on stretch via the hands crossing the front of the body - you can only go so far - and then to continue the motion you get a larger portion of arm elevation and clavicle elevation. Simple put in regards to where the hands move in relation to the body- it's across and then up.
If instead of pulling across and then having that effort turn to more elevation - assume you lifted your left hand from address out in front of you so that the left arm was parallel to the ground- and then brought it across your body to the "top" position- you'd notice that you eliminated or couldn't engage as many back muscles to help you during the downswing. So the hands move across the body and then as they run out of room get pulled up. If you move the hand up and then across - as in my example - you don't engage the lat muscles etc. for you to pull you down.
The action of the left arm moving across the chest is called adduction. A normal motion of moving the arm across the chest with a golf club also incorporates some internal rotation of the humerus. Adduction and internal rotation are actions of the lats and parts of the deltoids and rotator cuff muscles. So, in your example the lats and shoulder muscles are "activated" in both cases.
I think the cause has more to do with using two levers(arms) that have origins(shoulder joints) so far apart coupled with a rotation of the "T" shape made by the spine to the shoulders relationship as well as the action of the elbows and wrists that make it easier to make a "double or triple plane shift" motion when holding on to a stick(golf club). On the downswing the tilt of the axis that allows for precision and a more powerful delivery of the clubhead also adds to the plane shift(ing).
On the issue of power one may have to look more into length of travel for the hands and club head which allows a longer time for muscles and the pivot to accelerate the club head as well as the use of gravity. But, there are some shortish backswings that produce a lot of power due to float loading--but the float loading may cause a plane shift.