I'm cross-referencing @
TCinVA's excellent post in the
searching with WML thread, highlighting the text in bold below. Always tracking the gun with your eyes is a terrible idea for competitive shooters as well. A key skill in practical shooting is embracing the sequence of 1) getting your eyes to the (next) target as fast as possible, 2) looking exactly where you need to shoot, 3) moving the gun, 4) seeing the dot or sights arrive on target, and 5) breaking the shot after confirming the dot/sights appropriately for the target difficulty.
Moving the gun rapidly so the dot/sights appear exactly where you're looking is a core skill that requires significant practice. At last weekend's USPSA match, there were two Open shooters on my squad who have been in the sport for decades. Both "lost" their dot multiple times on stages, and it cost them dearly. My former coach had no patience for that, and would assign 100's of daily dry reps if that happened.