Gabe Suarez explained it well when he pointed out that: If you're CONCENTRATING on the front sight, you won't jerk the trigger because your mind really can't focus on the trigger pull and sight alignment at the same time. He's correct when he points out that few shooters understand that basic principle, as evidenced by the many different opinions on why we concentrate on the front sight.
Things are different in rifle shooting, since the sight is far enough away that both the target and sight are pretty close to being in focus.
If you don't concentrate (for us old geezers, it may not be in focus) on the front sight, you tend not to follow through. There's a delay between the time your brain says "shoot" and when you actually do.
You drop the gun and the shot goes low and you don't understand how you missed the target. "Dang, the sights were right there when I shot".
NO! your sights were right there when your brain said shoot, but not when the shot broke--you gave up and quit because you thought your job was done.
Same principle applies to the wingshooter who stops swinging when his brain says shoot and doesn't keep swinging. He shoots behind the bird.
Dont forget, the rest of the sight picture is important, also, even if rear sight is fuzzy (and it will be). Top of front sight even with top of rear, with equal amount of daylight on each side of sight. If you aim with dot, instead of top of sight, then that's an adjustment you have to make. Either put the dot on the target with the sight picture described above, or raise the dot so it's center is even the top of the front sight. Depends on how the gun zeroes.
I like the dot because it provides quicker target acquisition with my eyes. The squared sight is more precise, which my eyes can no longer take advantage of.