Another interesting result of the shoulders down cue is that it limits range of motion in shoulder flexion. There are but a few people that can achieve full 180 degrees of flexion at the gleno-humeral joint with a depressed scapula. Try Warrior 1 with shoulders up and shoulders down and see where the humerae situate themselves. Almost all of you will have your shoulder angle go from 180 to 165 degrees. Now re-orient this position upside down. In an inversion you either compromise position by over-extending the spine (a yogini favorite) or you actually upwardly rotate and elevate your shoulders despite your years of training.
So why the direction to depress them when in Adho Mukha Vrksasana? It is probably an artifact of the Mysore palace where Krishnamacharya watched young english soldiers practice gymnastics. If you follow the history of artistic gymnastics, you will see an evolution of the handstand from a banana-shaped or yoga handstand to a straight vertical handstand—-the modern handstand. Gymnastics evolved as the physical demands of gymnastics increased. The initial banana-shaped handstand is easier to balance and more accessible for people with tighter shoulders (older men in the military and modern yoga practitioners). As the entry into gymnastics got younger and the physical skills became more demanding the straight body handstand became the default. 180 degree shoulder angle and a straight body simply supports more weight (bone stacking) and allows for more advanced skills.
Sadly yoga teaching is more the stuff of mythology and religion than science so there still remain many cues that are passed down from teacher to student without further investigation. Watch this video and see for yourself.