There are several physical characteristics that can directly influence the plane the club travels on, as well as, the orientation of the club face during the swing. Mobility in the trail shoulder (right shoulder, for right handed golfer) is one of the most important.
The position shown in the left hand picture, demonstrates the most stable position for the trail arm. The weight of the world can be supported with the trail arm more vertical. Indeed, many coaches have used the analogy of atlas holding the weight of the world over his head to visualise the positioning of the trail shoulder. This is also the most common position seen on the PGA and LPG tours today.
If the trail shoulder can’t get into this position due to a physical limitation, typically lack of general shoulder mobility, thoracic mobility and/or shoulder external rotation, then a more horizontal trail arm will be seen. This will also often result in a higher swing plane than ideal and/or the club travelling across the line at the top of the backswing position, as shown in right hand picture.
The player has two choices. Adopt a less than ideal position of the trail arm in the swing or change their physical abilities. Below are some of my favourite exercises for increasing shoulder mobility:
Adding in some soft tissue work for the pecs is also a great way to manually improve muscle fascia and get back some range of motion in the shoulder.
And make sure to balance all pressing movements in your program with rows also. A 1:1 ratio at least, although for those who lack shoulder mobility 2:1 in favour of rows is probably closer to the mark.