In any other species of ant, if they had majors with jaws like this, that would be what the species was most famous for. But the Saharan Silver Ant (Cataglyphis bombycina) is far more famous for being the fastest ant when it comes to running and navigating.
Though really, this ant has always sounded like something a 10-year-old made up. "They are silver and and they live in the desert and and they only go out at the hottest time of day and and they are the fastest ants in the world and and they have majors with GIANT jaw and and--" These ants are just too cool. (or too hot)
What I would like to know is what is the deal with these majors and their extreme jaws? The majors don't generally go on the mid-day food runs-- but maybe such big jaws could help if the ants stumbled on a huge bounty of food, like a small lizard or something. It's also probably about defending the nest as in videos about these ants you see the majors hanging around menacingly near the nest entrance. That said, I have not seen much about their bite. I don't even know if they'd try to bite a person if provoked.
One theory that I have is the majors just look scary. You look at this ant and think "nope." and maybe that's the point.