In many movies, documentaries, and photos it appears that the troops did not use their straps. Considering the fact that so many pictures depict this, even in combat, there has to be a good reason. I read somewhere that the straps were too strong, so a large explosion could cause he helmet to rip off the head and cause serious damage with the strap on, but I can't find much more on this.
There's a couple things here. First, soldiers are more likely to be photographed in less dangerous situations, when they would also be less likely to worry about things like chinstraps.
Second, soldiers in combat feared that, should they engage in hand-to-hand combat, an enemy could grab the helmet from behind and thrust downwards, using the chinstrap to snap the neck. This may not have actually been a real risk, but like the fear of your head being ripped off by an explosion, the fear was there.
Third, and this is probably the biggest reason, chinstraps are annoying. It may not seem like that big a thing, but wearing that chinstrap for hours on end can get tiresome, and sometimes they chafe.
If the blast is big enough to rip a helmeted head off then it would kill the soldier regardless.