W_S said it exactly. When it comes to chin straps on snaffles, I live by the old saying "It's better to have it and not need it than need it and not have it". I don't own a single snaffle without one and I've been in several situations where it has kept the bit in place. I ride a lot of young horses and, as everyone knows, young horses are inherently unpredictable. Just because he rides nice and responds the way he should in the round pen or arena doesn't ensure that he'll respond the exact same when out in the pasture and a turkey flies within a few feet of his head or a coyote/deer jumps up out of the brush 5 feet away. Heck, I've even had really nice, responsive, calm horses go into a bucking frenzy the first time they got poked in the flank by a bush we were riding past. In times like that, the first thing to do is ensure my own safety, even if that means really taking their head hard and fast to the side.
IMHO, any person is simply lucky if they've never been in a situation where a small little piece of "possibly meaningless" safety equipment has saved their lives.