You're arguing against a strawman. See the final chapter of Our Enemies in Blue by Kristian Williams for more details on possible alternatives, including historical examples. And the whole book makes a compelling, intricately cited argument for police abolition.

The fact is, the police do provide an important community service—offering protection against crime. They do not do this job well, or fairly, and it is not their chief function, but they do it, and it brings them legitimacy.[1584] Even people who dislike and fear them often feel that they need the cops. Maybe we can do without omnipresent surveillance, racial profiling, and institutionalized violence, but most people have been willing to accept these features of policing, if somewhat grudgingly, because they have been packaged together with things we cannot do without—crime control, security, and public safety. It is not enough, then, to relate to police power only in terms of repression; we must also remember the promise of protection, since this legitimates the institution.

Because the state uses this protective function to justify its own violence, the replacement of the police institution is not only a goal of social change, but also a means of achieving it. The challenge is to create another system that can protect us from crime, and can do so better, more justly, with a respect for human rights, and with a minimum of bullying. What is needed, in short, is a shift in the responsibility for public safety—away from the state and toward the community.

It should be noted that Williams is working under a tweaked definition of "crime" in this context, a phenomenon that anarchists do not deny exists.

The point here is that the standards I want to appeal to in invoking the idea of crime are not the state’s standards, but the community’s—and, specifically, the community’s standards as they relate to justice, rights, personal safety, and perhaps especially the question of violence.

All emphases mine.