You sound like you know what you’re talking about, but I’ve been shooting my entire life, and I’ve never noticed that I’m focusing on the sites or the target separately, both seem to be in equal focus for me. Perhaps I’m switching back and forth rapidly, but if so, that is imperceptible.
I didn’t just imagine the accuracy and reaction times of the average soldier, that’s the requirement to qualify with a rifle. You have to hit a certain number of targets out of 40 targets, that pop up randomly over varying distances and then go back down when you either hit them, or too much time has lapsed. At 300’ the target is up for 2.5 seconds before it goes back down. The targets are up for shorter durations as they get closer to the marksman. Or at least that’s how it used to work when I was in the Army a couple decades ago.