The reason The Perfect Pistol Shot recommends handgun shooters keep both eyes open is perspective. The human eye is designed to work as part of a pair. Close one eye and the objects in your vision appear to shift. Switch eyes and vision swings an inch or so in the other direction. Triangulating the front sight tip between both eyes’ focus ensures a truer positioning of the sights.
Defensive use of the handgun requires situational awareness. Defenders must collect as much second-to-second intelligence as is reasonable. In other words, if you close one eye, you are half-blind to potential danger.
Some shooters have pronounced vision problems that prevent two-eyes open. Obviously, the shooter must adapt to reality but shooting with one eye closed out of habit is a self-imposed handicapping of your shooting ability.