Alexander knew the Iliad by heart. He loved Homer, and always slept with a copy of the Iliad under his pillow. His first teacher was Leonidas, a relative of Olympias. Leonidas instilled in Alexander his ascetic nature for which he became famous during his future campaigns; he lived simply, in a Spartan way, eating and sleeping together with his troops.
In recent years, they've increasingly insulated themselves from the danger even the average person faces to the point where the president and congress will likely be found 250 feet underground in a hardened bunker somewhere in West Virginia at the first sign of trouble.
This guy is willing to take a little risk in making this gesture, and the effect won't be lost on the troops.