What kind of crime is preventable or non-preventable by a government? And what reasonings to justify it.
All crime is preventable by government.
Implement nuclear holocaust, exterminate all human life, crime rates drop to zero per unit time.
Well, maybe that's not what we want to do. Maybe we want government to guarantee certain rights. Say one of those is the right to life (the government loses the death penalty).
Sterilize all humans. Wait for the second to last person to die. All crime rates drop to zero per unit time.
Okay, maybe we need a right to procreate.
Distribute all humans in such a manner they can never interact with each other, but provide for IVF. Without the possibility of any human interaction, all crime rates drop to zero per unit time.
Perhaps we want to have a right to live anywhere we choose.
Sedate all humans such that they are incapable of any action. All crime rates drop to zero per unit time. This method requires autonomous care-takers.
These might seem like unreasonable arguments, so I would ask - what is the fundamental philosophical difference between between these methods and a totalitarian police state? To me, there isn't one, and one of the reasons I think this question even came up is that some people today live under governments that do not guarantee sufficient rights that they have rights as a reason to not guarantee zero crime. The point being, all crime is preventable by government.
What then, are the restrictions on crime prevention:
Cost. Governments often struggle with funding and efficiency. Sterilizing 300 million people isn't cheap in the first place, but ensuring the 100% compliance required is even more difficult. And note, as more and more rights are afforded, cost of prevention increases. At a certain point, costs of enforcement grow greater than GDP and enforcement becomes impossible even in a 100% efficiency system.
Conviction. Governments under the democratic paradigm are beholden to their people, many of whom value living out from under severe oppression associated with maximal enforcement. For example, many nations afford freedom of religion, which can make enforcement more difficult. However, I know I personally would attempt to emigrate from or overthrow the government of any nation I lived in that did not provide freedom of religion. These fear of overthrow or exodus limit the operations of government.
Corruption. Governments, in general, must develop some form of enforcement agency. However, these agencies also need to be enforced, and tend not to want to enforce themselves. Of course, you can create an agency to enforce the enforcers... In general, this places practical limitations on enforcement. Enforcers need some level of power to enforce at all, then this power makes them more difficult to enforce. Providing less power requires more enforcers, etc.
Governments optimize in their finite capacities (note I do not say resources, as governments may attempt to make provision for additional resources) according to some social utility curve. Generally this curve has safety on one axis and rights on the other. With absolute rights, you have no safety (right to murder, right to torture, etc). With absolutely no rights, you can provide complete safety.
To me, the only legitimate criticism of a government operating under the charter of its people is that it is failing to reach any one of the infinite instances of Pareto efficiency, that is, it could provide greater rights with no safety trade-off or vice versa. Arguably, you could say it is selecting the wrong Pareto efficiency, but I would argue that this is a failure of representation and not of enforcement.
In the case of Pareto inefficiency, the government should be held accountable for some mixed set of the crimes that it could've prevented or rights it could've afforded up to Pareto efficiency and then no others. It can also be held accountable for any sub-optimal conditions deriving from its own inefficiencies.