I think the DMG has exactly the wrong reasons for Group Checks (which I usually really like).
It should be a tool to make some group attempts interesting instead (near-)automatic misses or successes. It's not only tied to stealth, but also to knowledge or perception checks, where a singe success mean success for all .. so there is no reason to even roll if you have a normal or large group, even if no one is trained in such things.
I always see group-checks as someone good is helping someone who is bad at the task. Like letting the best at sneaking in the front and everyone is following silently in his footsteps, or testing the group-knowledge of Arcana, climing a mountain together where the best Athlete is moving forward securing the rope..
This makes for good group activities that bond the heroes together instead of leaving most behind (sneaking) or everyone needlessly chiming in because a single good roll is needed (knowledge). It might not be the most realistical rule, but one that helps with some skill-related problems that plague rpg's since forever.