An example I tend to give is the case a while back where someone was wielding an axe. Two police officers went after him, and the axe-wielding man was shot and killed because he went for one of them.
Success, surely? He protected his partner, who might have been harmed.
The way something like this would likely have gone down somewhere like the UK would be that the first responders would have called for reinforcement, and then kept their distance and waited. You don't engage someone armed unless there is immediate danger to others. She should never have been close enough to be in danger.
In the UK they may or may not call in a firearms team in such a case, but if they did, they'd be brought in as a precaution. More likely they'd close down the area around him and wait, and wear the guy down, and then see if they could get him to drop the weapon peacefully.
For comparison there was a case of a man robbing a house near me a while back unarmed, and the police brought in 20 officers, chased him until he climbed onto a roof. Then they simply waited for 4-5 hours until he accepted he had no way out.
So many of the cases I hear about from the US is down to impatience and seemingly some kind of belief that they need to stop things as quickly as possible rather than trying to stop things with as little conflict as possible.
I don't think it's necessarily so much punishment as fear that if they don't do something, things will escalate. But most of the time if you contain a threat and wait, the level of conflict will de-escalate. So much violence boils down to fear that the other side will be willing to use more violence. And that fear is pervasive through some groups of people. E.g. we see that in the insistence of keeping or carrying weapons.