...and police are trained to just unload the clip because of that.
Cops aren't trained to dump their clip because of pistol accuracy. They're trained to unload because the presumption is that if a firearm is drawn and used, they're in a life-or-death situation, and the objective is no longer to neutralize a target, but instead kill them. This is one area in which we're still stuck in mid-'90s insanity, because since then +P, hollowpoint, and center post rounds have become more or less standard among police forces and training methods haven't kept apace.
Your run of the mill, 115 or 124 grain, 9mm FMJ round just doesn't have a whole lot of stopping power. They're great for (over) penetration, but when it comes to transferring force to a target or deforming, they fall short; meaning, they're likely to go through-and-through and cause a less-severe wound than even smaller calibers. Shot placement is
always king, but in an emergent situation against a moving target you can't count on proper shot placement, nor on accurate follow-up shots, so the first shot (which you're going to be aiming center-mass) has to have maximum chance of putting your target down. When you start talking about those dinky 9mm rounds that were the rage in the early to mid-'90s, yeah you keep shooting until the target's down, and if that takes the entire clip it takes the entire clip - and it may damn well.
Here we are thirty years later, and we have
far more lethal 9mm rounds on the market than we did at the point LEO started transitioning to semi-auto, 9mm, nationwide. But, they still train as if they're using those rounds.
Cops
are trained to take follow-up shots regardless, but that's not a cop thing. That's an
everyone thing, all the way from special forces to your everyday dipshit who puts in the range time praying to god it never comes in handy. Even when I put in my range time (something I haven't had the chance to do since COVID) I do Mozambique drills, and my round of choice is 135-gr JHP.