Well, the reason we weren't shown things like certain character's deaths is because it contributes to the movie's themes.

Stop reading this if you haven't seen the movie.

Moss's death happening was a foregone conclusion as soon as he gave in to his "moral" side and went back to give the Mexican drug-runner some water, but having it happen not at the hands of the seemingly invincible assassin on his trail but offscreen to some Mexican gangbangers puts the lie to the assassin's story of how he is the avenging angel of fate. The movie starts off with some of the most explicit violence possible (Anton blowing a hole in someone's head or shredding a man's throat open with his silenced Tec-9) and then gradually dials down the violence to offscreen with the aftermath only shown (in the case of Moss's death) or offscreen entirely (when Anton goes to kill Moss's wife). It's not an action film where Moss and Anton are supposed to have this climactic gun battle, and really, Moss isn't even the protagonist: Tommy Lee Jones's character is, and the movie's sense of helplessness is amplified by having him not only fail to prevent Moss's death, but fail to even get there to witness it. By the time he arrives on any given scene, the action has long passed him by. The ending isn't going to have some huge action set piece, Jones's character didn't even carry a gun. He's just left behind to ruminate on fate and destiny and I like that a lot more then having the movie end with some ridiculous duel to the death between a redneck who stole a drug dealer's suitcase and Anton the master assassin.