Since I’ve gathered some data on the topic in the past, I am going to link to a Lucky Gunner article about using the sights on a pistol.
I did an experiment years ago in which 10 different experienced shooters tried point shooting a single round at a silhouette starting at one yard. Then the distance was increased one yard at a time for the group. To test whether some form of visual indexing to the pistol was necessary, each shooter had a piece of cardboard placed horizontally in front of him at neck level so there was absolutely no visual reference to the pistol’s orientation. There was no time limit, the shooters were free to adjust their pointing until they thought they were on target.
The bullets starting hitting the ground at two yards. Only one shooter was able to make a hit anywhere on the silhouette at 5 yards and that was a peripheral hit. I discontinued the experiment at that point.
I figured out everything I needed to know about hitting a target without visual reference to the gun and with the gun below the eye-target line from that experiment.
Using the sights (i.e., getting the pistol into the eye-target line) is how we learn to kinesthetically index the handgun. Ask someone to point their finger at any object. Notice they don’t do it outside of their ‘workspace’ the more or less basketball sized space in front of the chest, properly called the ‘ipsilateral visual field.’
We may not always use the sights in a fight but training with them is how we learn to correctly index the pistol kinesthetically.