If sights are necessary for precisely placed hits, and police officers receive special training in the use of sighted fire, why can't they see them in the heat of battle?  There are a number of factors, but the most likely explanation lies in basic human physiology.  When a human being is suddenly scared, shocked, or surprised (as is the norm in a life-threatening situation) the body experiences the "fight or flight" reflex, and a number of involuntary physiological changes can occur. "Fight or flight" reflex is simply the activation and domination of the Sympathetic Nervous System (SNS) over the Para-Sympathetic Nervous System. 

The Para-Sympathetic Nervous System is in primary control of your body when it is not in a state of crisis.  It is responsible for functions such as the constriction of the pupil, the slowing of the heart, and dilation of blood vessels.

The Sympathetic Nervous System (SNS) is in primary control of your body when it is in a state of crisis, such as when facing a lethal force situation.  It releases adrenaline, which cause involuntary and automatic increases in heart rate, blood pressure, and blood flow to the extremities.  SNS activation can heavily affect mental processes, motor skills, sensory perception, and, particularly, vision. Three important visual aspects that are affected are reduced peripheral vision, distance-only eyesight and forced binocular vision.

Reduced peripheral vision, commonly referred to as "tunnel vision", often occurs in gunfight conditions.  Up to a 70% decrease in peripheral vision is normal.  Occurring with this is a highly reduced ability to detect subtle motions, such as that of the handgun's relatively small front sight bobbing in and out of alignment in relation to both the rear sight and the target.

Distance-only eyesight occurs as we instinctively focus on our threat.  Human instinct will cause us to focus on our threat during combat—this means our eyes need to be focused for distance.  It is theorized that this reaction is a result of SNS activation simultaneously dilating the pupils in the eye and relaxing the ciliary muscle (the eye muscle responsible for close focus) .  Even if distance-only eyesight does not occur, according to Guyton's Medical Textbook (and others), it takes about one full second for the human eye to switch from near focus to far, (as in shifting focus from the front sight to the target).  In contrast, a shooter of average ability, armed with a long-trigger-pull, double-action revolver, can fire three rounds toward a target in .75 seconds .  This is an unacceptably long delay in the rapidly changing, dynamic situations like gunfights or competitive shooting events.

Forced binocular vision means that we square our heads to our intended target (the threat) and we focus on it with both eyes open.  This is the body's way of forcing more light to the retina. We also have a tendency to crouch and face the target squarely under stress and SNS activation.
So, generally speaking, when a person is in the grips of SNS activation, that person is facing the threat squarely, intently focused on it and with a reduced ability to detect small movements and near objects, regardless of how he or she has been trained. Under these circumstances, traditional sights become difficult, if not impossible, to see.

The SureSight™ simplifies aiming by causing the shooter to make a picture, rather than align meaningless notches and posts.  Since we know that simpler is better, this is a positive enhancement.  The SureSight's™ shape capitalizes on the Gestalt Principles of Perceptual Organization, which state that human beings have an inborn ability and tendency to complete shapes.  The SureSight's™ front sight is also designed with ease of use in mind.  Being shaped like an arrow, it takes advantage of everyone's natural conditioning to point arrows at objects.  (Remember, the front sight is the most critical to accurately placed shots.)  In fact, in preliminary tests on people completely inexperienced with handguns, aiming with the SureSight™ was immediately self-explanatory to all of them. This is not true with notch and post sights. (And for the advanced shooter, this system was universally faster and simpler for all that have tried it.)