My personal observation is that a hand around a BTFE is less obstructive that a hand around a set of barrels. Try it. For competitive clay shooting, give me a BT every time. If shooting doubles, the BT offers much needed protection from hot barrels.

As to the extended arm seen on the long ago shooters, it may partly be style, and it might be function. Most of the old gun stocks had more drop and less pitch, both conditions contributing to muzzle rise. Do a force diagram and it becomes pretty clear. I don't think Zutz ever took high school physics.