In my opinion, the benefit to the wind-up is that tempo can be established and momentum built up more slowly (and possibly under more control) using a "running start". To achieve the same tempo and momentum from the stretch, the pitcher has to start forward more explosively to get up to speed more quickly. Many coaches think young kids should pitcher from the stretch only because there is less movement that might lead to balance issues. But I think when young kids try to be more explosive, that can also cause more movement as they maneuver their bodies into that position from which they can explode (e.g. collapsing the back leg to push off the rubber). So I really think the "less movement" thing is really a wash.
Furthermore, many young kids start off doing what they see the pros doing (most pro starting pitchers pitch from the wind-up). Thus, by the time they get to organized baseball, they are more practiced and, therefore, more comfortable from the wind-up. And there's a lot to be said for comfort. But not all kids are more comfortable from the wind-up.
BTW, there is one pitching expert out there who is pushing tempo and momentum to an extreme and, based on what I've heard, this seems to work better from the windup than from the stretch. It's a stretch but maybe your son's coach is a follower of this expert and is positioning your son use this expert's mechanics.