Having been through police training, I absolutely agree that better training for police is important, but there are several problems with your argument.
First of all, accurately firing a weapon requires one to relax, breathe slowly, reduce the heart rate, hold still and concentrate. Almost all situations that justify shooting at people involve imminent danger of death to the shooter, the shooter's allies or innocent bystanders. That pressure produces a physical response exactly the opposite of what's required to shoot accurately. Good training can partially compensate, but it's impossible to replicate the psychological and physiological effects of the possibility of imminent death without a significant risk of actual imminent death.
Secondly, non-expanding ammunition will easily penetrate through a person and retain enough power to kill a second person. In most cases, a single bullet could kill three or four people if they were properly aligned. Ideally, the shooter will try to make sure the bullet will stop safely after penetrating the target, but circumstances that require shooting people are rarely ideal. Using bullets that are easier to stop is better for bystanders.
Finally, bullets do a surprisingly bad job of instantly physically incapacitating people. There are a number of cases on record of violent criminals continuing their attempts to murder police officers after being shot multiple times, even after receiving wounds that aren't survivable even with immediate medical treatment. Most people stop fighting when shot for psychological, not physiological reasons; they didn't like being shot and don't want it to happen again, the pain is too severe to continue resisting or they hope that giving up will lead to medical treatment and a better chance of survival. Barring that, there are three ways a bullet can incapacitate a person: damage the brain or spinal cord enough to prevent movement, cause enough blood loss that the brain shuts down, or damage the heart enough that it can't pump blood to the brain. Expanding bullets have a higher probability of causing these effects than non-expanding bullets.
Fair point about the difference between immediately incapacitating and unsurvivable. I think the different amounts of danger presented to a bystander that is only hit once is still worth at least investigating though.
I think it is definitely worth considering if reliance on expanding rounds that are not perceived to penetrate has an effect on the tendency to take risks in situations where there are people behind the target. As I see it, considering the number of shots often fired by police and their poor accuracy, it doesn't really matter that the rounds won't go through multiple people. The more accurate police are, the more fragmenting rounds start to seem sensible to me.
Being concerned about bullets going through badguys and hitting innocents or hitting multiple innocents in a row instead of just one seems like... premature optimization.
It's worth looking at. The standard introduced by the FBI and used by many law enforcement agencies is 12-14" of penetration. That's enough to penetrate most people front to back and still be dangerous to someone behind them. It would be unreasonable for anyone in law enforcement to assume that such bullets don't present a risk to bystanders. If anyone does believe that, they need different training.
The issue here, which was introduced by the FBI after their infamous 1986 Miami shootout, is that at worst case you have to shoot through someone's arm and then penetrate to the vitals (especially heart). Obviously that's going to over-penetrate front to back, and it's occurred to me the worst case that way is if you only hit a lung, plus of course whatever happens with the ribs. I would expect most self-defense expanding rounds to go right through with a lot of retained energy depending on what happens around the ribs.
From Wikipedia on the FBI shootout, matching my memory of various accounts:
"As Platt climbed out of the passenger side car window, one of Dove's 9 mm rounds hit his right upper arm and went on to penetrate his chest, stopping an inch away from his heart. The autopsy found Platt’s right lung was collapsed and his chest cavity contained 1.3 liters of blood, suggesting damage to the main blood vessels of the right lung. Of his many gunshot wounds, this first was the primary injury responsible for Platt’s eventual death."
He was functional for quite some time after that, including killing the two agents who died in the shootout. Here's some illuminating details from the end of that section:
"[...] The bullet penetrated Platt's chest and bruised the spinal cord, ending the gunfight.
The shootout involved ten people: two suspects and eight FBI agents. Of the ten, only one, Special Agent Manauzzi, did not fire any shots (firearm thrown from car in initial collision), while only one, Special Agent Risner, was able to emerge from the battle without a wound. The incident lasted under five minutes yet approximately 145 shots were exchanged.
Toxicology tests showed that the abilities of Platt and Matix to fight through multiple traumatic gunshot wounds and continue to battle and attempt to escape were not achieved through any chemical means. Both of their bodies were drug-free at the time of their deaths."
Yikes. And there are more incidents like this one.
First of all, accurately firing a weapon requires one to relax, breathe slowly, reduce the heart rate, hold still and concentrate. Almost all situations that justify shooting at people involve imminent danger of death to the shooter, the shooter's allies or innocent bystanders. That pressure produces a physical response exactly the opposite of what's required to shoot accurately. Good training can partially compensate, but it's impossible to replicate the psychological and physiological effects of the possibility of imminent death without a significant risk of actual imminent death.
Secondly, non-expanding ammunition will easily penetrate through a person and retain enough power to kill a second person. In most cases, a single bullet could kill three or four people if they were properly aligned. Ideally, the shooter will try to make sure the bullet will stop safely after penetrating the target, but circumstances that require shooting people are rarely ideal. Using bullets that are easier to stop is better for bystanders.
Finally, bullets do a surprisingly bad job of instantly physically incapacitating people. There are a number of cases on record of violent criminals continuing their attempts to murder police officers after being shot multiple times, even after receiving wounds that aren't survivable even with immediate medical treatment. Most people stop fighting when shot for psychological, not physiological reasons; they didn't like being shot and don't want it to happen again, the pain is too severe to continue resisting or they hope that giving up will lead to medical treatment and a better chance of survival. Barring that, there are three ways a bullet can incapacitate a person: damage the brain or spinal cord enough to prevent movement, cause enough blood loss that the brain shuts down, or damage the heart enough that it can't pump blood to the brain. Expanding bullets have a higher probability of causing these effects than non-expanding bullets.