I presume you mean the old "Andy Devine" School of Shooting, where you use the pistol to help throw the round at the bad guy? (OLD, OLD Western actor), every time he fired his weapon went up and back and he would then throw it forward and fire, It Allways looked like he was not shooting so much as trying to help the round go faster or was simply thinking if he snapped the gun down ad forward fast enough the weapon would fire the round for him and he wouldn't have to remember the cock and fire it.
Hey like I said everyone seems to have different ideas about what stance is the correct one, double taps, triple taps. The thing I like about what I described, is if you are doing EP or something equally as dangerous if was possible the bad guys were wearing vests and so should you. And since there really is only once place basically to put a round into the front of someone's head it makes for a very small narrow forehead to aim for, I real life unless that is literally an automatic unthinking mussel trained shot it's hard to do in a fire fight especially your first. If you shot someone in the face you might get the round all the way to his brain, but then you may not, because there is too much teeth and thick bone to get through and or deflect the shot.
So if you learn to go 2 in the center mass you may or may not kill the opponent, so then your back up shot becomes instead of the narrow forehead, the groin area. much bigger target and easier to do damage to. Which forces the opponent to lean forward, which brings the entire top of their head into the target area. Way easier to hit than the forehead and the added bonus of doing a Hugh amount of damage to the brain and most likely other vital places.
Granted this shot and some others may not be a good idea for civilians let alone LEO's because of archaic rules about letting the bad guys out arm you and then get wrapped in the "innocent until proved guilty mantle". But when you are fighting for your life or your loved ones lives then thinking outside the box is a good idea. They hide behind walls, shoot the damn wall, so it gets messed up? who cares a little spackle and some paint and no one no except the bad guy that thought a sheet rock wall was a good place to hide, Same for furniture, shot through it. Not a lot there to actually stop multiple rounds for getting at least one through. If you are outside, drop to the ground and look Under whatever there is between you and them. You might get lucky and get in a foot or leg shot
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I'm going to ruffle more than a few feathers with what I just said but think of it like this. Back in the day Armies thought that standing in a nice round in the open wearing colorful cloths was the only legitimate way to fight with honor. Sort of like mass dueling, They also thought that commoners taking out an Officer (Generals mostly) Knight or Royalty on purpose was totally outrageous and uncivilized. Ya well somewhere around 1776 the world woke up to the fact War was not a nice tit for tat Mass duel with rules and tea at 2pm. It's taken a while to get through to some folks that still think war is Honorable, NO it isn't, Fighting for your Family, Friends and Country is Honorable, war itself just sucks and the only thing that counts is surviving, and if that means shooting someone in the back then count on it, their dead. There is not one damn thing Civilized about war and killing people, most of them are the exact same as you, they just speak differently. Doesn't mean you would drink with them in "peace time". They are there for the same reason you are, because the politicians insisted the Diplomats are complete a-holes, and you/they drew the short straw. So they want to go home just as much as you do, but that most likely isn't going to happen, Somebody, Allways dies. Just don't let it be you