The type of personality that serial killers have is not exactly conductive to discipline and good order; most serial killers who served either had extremely mundane service in times of peace or in non-combat roles, or they had their service cut short because of psychiatric or disciplinary issues.

Besides, there's a difference between killing unarmed people who either can't defend themselves or can be overpowered, and killing armed men in the middle of a firefight. These guys are cowards, they don't want to actually risk life and limb to kill.