Let us take violence to mean "physical force used on another person without the other person's consent," and police to mean "agents of a national government authorized by that government to use violence on behalf of the nation."
Violence is a problem because it hinders the victims' attempts to be kind to themselves, and it leaves the perpetrators in need of redemption. However, it is the case that people intentionally act to hurt each other under certain circumstances that cannot be reliably avoided. Therefore, violence will continue to recur at some level for the foreseeable future.
Reducing the problem of violence is important work for humanity. It is work that has been done for thousands of years: there is much from the past to draw on. In nearly every area, there are societal structures created with the purpose of lowering the amount of violence that occurs.
In areas that are stably controlled by a nation, one major structure filling this niche is national police forces. Police forces typically act to reduce violence by separating violent acts into criminal and non-criminal categories and taking various measures to prevent the criminal ones. Police forces use violence, among other tactics, in an attempt to reduce violent crime. The intended effect is that the violence used by police causes less total damage than the violence the police prevent.
There are two major ways in which policing can fail. One is that the police can be too markedly active. They are a group that is authorized to use violence on behalf of a nation; they can use too much violence, or the wrong kind at the wrong time, and thus cause damage that is not directly related to a larger preventative effect, i.e. excessive force.
The other is that the police can be too markedly passive. They are the only group that is authorized to use violence on behalf of a nation. To the extent that they disrupt the formation of a new national government with the police powers that the people of the nation demand, they take on the responsibility of being the police powers that the people of the nation demand.
The first failure mode is one that every person is vulnerable to. Anyone could use violence in an attempt to reduce violence and end up causing more problems than they solved. It's a significantly stronger risk for people who are already committed to the use of violence to reduce violence, but it's not a special problem; it's the usual rules, just applied to people who by the nature of their role have to skirt the edge of said rules.
The second failure mode is not universal, and is specific to police. Most people don't have the mark of "person who stops communities from defending themselves" and thus don't require the counter-mark of "person who is obligated to defend communities they have made helpless." In effect, police are a special case of guardian-ward rules.
I am aware of the grim aspects of the history and present of policing in my country, the United States. I am aware, at least in a general way, of such things as institutional prejudices and unjust laws and abuses of power and the places where internal policy holds out over even the courts. I do not hold myself responsible for it, but when I am called to patriotism, I make sure to remember also our national shame.
I do not think policing is avoidable. I think that I have an inkling of what happens when everyone knows whatever disorganized response the people involved can muster is the only power demanding accountability from anyone who attempts violence. I think that the system of authorizing government agents to use violence in ways preapproved by people who are not in the heat of the moment prevents countless atrocities, and that it cannot be safely dismantled for the indefinite future.
In any case, disbanding the police force all at once through some trickery would do nothing but ensure that it returned after a tumultuous period in which many people's lives were disrupted for no benefit. The process of isolating the interventions which are productive to the cause of reducing violence is slow. Humanity's current knowledge of the phenomenon holds that a competitively efficient set of methods must include a special category of people who are authorized to use violence to implement policies under some circumstances.
Given the harms done by violence (both intervention violence and the violence being intervened in, combined into a single entity), I want to find out more about that phenomenon. I want to know what the most efficient intervention set is so I can tell my nation to direct its police to enact them and no others. I want to let my patriot's heart make a nation I can be proud of more readily, with fewer reservations. And I want to spread the information humanity reveals, so that the people of every nation have the tools they need to be kind to each other, and to encourage each other to be kind.