//…jail which hasn't worked for over 200 years.//
Jail does work. For the term of their incarceration, the rest of society are given a break from the effects of the miscreants’ activities. That should be seen as its overriding (and in most cases, sole) function. You’re surely not expecting it to “rehabilitate” prolific or serious offenders, are you?
//…or deaths would be a daily occurrence.//
Deaths are a daily occurrence. In 2019 there were 671 convictions for murder and manslaughter. That’s getting on for two a day.
The police do not need to “work with perpetrators”. They need to prevent them committing crimes and if they cannot do that detect them and bring them to justice. That is their overriding function. They don’t need to understand why they commit crimes. I can tell them the answer: in most cases it is because they are disposed towards criminality. That’s all they need to know.