I think the idea of the followup shot isn't because the muzzle flash has been beneficial, but because as Jeff pointed out about night vision being ruined, but because that is the last thing you are going to be able to see for a while. What appeared in the flash is now your last known target location.
JMusic, the tactic sounds pretty stupid from a control standpoint. In real life, that second shot will most likely miss the target and you will then be left standing blindly in the dark, wondering what bystander you shot down range.
Take your 870 example. The first shot lights up things and shows the relationship between you and the bad guy. Let's say you were 4" off as you noted and so you pump the 870 and then fire the second shot making the 4" correction. While that sounds wonderful, it isn't.
Was the first shot 4" off the target? If so, you screwed up.
Was the first shot 4" off from where you intended, but on the target? If so, you now have a bad guy that has been hit by a shotgun blast. Just what do you think the odds are that the bad guy you just shot is going to be standing in the same place by the time you get off your second shot? Chances are, he is either going down or moving laterally, but not standing still. You will end up with an "incredibly accurate" second shot that will completely miss because the bad guy is no longer present in the position he was during the first shot.
I have no doubt that the technique is/was very effective for non-living stationary targets. I equally have no doubt that the technique is extremely dangerous and irresponsible as you are firing the second shot at a last known location without the ability to see if the target is still present there or not.
What was that rule? Know your target, backstop, and beyond?
For the second shot, you won't know your target as it moved. You won't know the backstop unless it is in the immediate flash vicinity. You definitely won't know what is beyond because the flash didn't illuminate very far down range and now your night vision sucks.