And you can focus on the target, not on the front sight.
WHY would anyone do this? This is teaching the exact opposite of good pistol shooting. If you are saying do this
sometimes, why are you trying to train yourself to do two different things?
Front Sight, Press -- Front Sight, Press
To those who say it's hard to pick up the dot: Where are you looking? The dot falls where the weapon is pointing! Close to where the sights are lined up, if you happen to be looking down the sights. And if you're practicing good gun handling, it's stock-still, not "bouncing" around!
I watch people at the range using lasers and they are literally NOT looking at the pistol. They are looking at the target and waving the pistol around like a laser pointer trying to see that dot show up on the target.
If the practice is to present the gun correctly (4-count draw) press it out and see your front sight on the target -- then voilà! There's the red dot on target, too. But you've already got to BE on target for that dot to appear there. At that point it is redundant and (to me) distracting.
In practice, what I see is shooters drawing the gun, peering PAST it, and looking for that dot, making adjustments with the gun to put the dot where they want it and then trying to hold it still while they press the trigger. Usually (in the case of some shooters I know well) they could have already landed at least two shots with their iron sights before they get the dot just where they want it.
And if you're practicing good gun handling, it's stock-still, not "bouncing" around!
This sounds like slow-fire bullseye shooting. Not like any defensive or "practical" shooting I've ever seen or done. Secondly, defensive shooting isn't about ONE shot, but about putting as many accurate shots on target as possible, as quickly as possible. For a good shooter this can approach 5 aimed shots per second. No, your dot is NOT sitting "stock-still" while you're pistol is recoiling every 0.2 seconds. You absolutely, positively, 100% guaranteed, cannot track a laser sight dot at rapid fire speeds. It cannot be done. Watching someone TRY is painful. Like watching a dog try to run with two legs tied together.
However, you absolutely CAN track your fixed front sight that fast, as many of us demonstrate every time we hit the range for training or competition.