Hey, new to this forum, but thought I'd take a crack at Clemlaw's question. There is a leadership theory out in the non-BSA world that follows EDGE quite closely. It's called situational leadership. It's practically a mirror of leading EDGE. I think we use the term EDGE because it's easy to look at the acronym and remember the steps.
As to why a scout has to use teaching EDGE to teach another scout how to tie a square knot? The principles of tell, show, guide, step back and enable are proven teaching techniques that are invaluable for a boy to learn if he is going to become a leader. ALSO it ensures that the adult advisors know it, hopefully from Woodbadge at least, so they don't get stuck in the ED...only part of it.
Critical part of EDGE and situational leadership is training to understand how to recognize where on the EDGE or M1,M2,M3,M4 scale the learnee IS and modify your leadership/teaching approach to help them learn.