Why use a backpedal in field or box lacrosse?
1. Allows player to keep the stick in his strong hand
2. The body shields the ball from the defender
3. As Jordan Ruggeri noted, the backpedal sets up a redodge to the middle which is prime shooting real estate
We'd rather our players keep the stick in their strength as much as possible rather than switching to their off hand especially when it comes to shooting the ball. The emergence of box lacrosse at the youth level in America has taught us there are multiple ways to shoot the ball from your strong hand when before we thought using your off hand was a better idea. Even before box lacrosse invaded, there had to have been players that felt more comfortable shooting a right handed BTB than a "normal" left handed shot.
Youth players unknowingly use box tendencies because of a general refusal to put the stick in their off hand. By teaching them why and how to set up their strong hand more often, see the backpedal, they will be a more effective player at a younger age. If you're more effective, you're going to have more success and if you have more success you're going to have more fun.
If you're a youth coach, would you rather watch a U13 player with one year of experience struggle and resist trying to improve his weak hand or enjoy trying to learn how to score behind the back?