I can see the rationale, but I disagree.

I think it's difficult to make a good assessment because every situation involving multiple legitimate armed factions that's come about has had a lot of other Context around it that makes it hard to know if what you're seeing is because of the factions, or because of the context.

That being said, the vast majority of cases I can think that involve multiple armed factions seem to devolve less into rational actors minimizing conflict to reduce cost, and more into rational actors executing violence to maintain control of resources or impose conformance with their beliefs.
Violence is often very profitable. It gives you control over resources you didn't have, and compels people to cooperate with your wishes.

they also couldn't legitimize the violence

In the absence of a monopoly on violence, all of it is just as legitimate. Each group sees their use of force to further or protect their interests as legitimate and others as illegitimate. This can manifest as blood fueds, vendettas, communal violence, or the myriad forms of organized crime.

I totally agree that the leviathan, which is a much cooler word for the entity with a violence monopoly, has no reason to offer overmuch quality to their violence. The leviathan only wants to use force to perpetuate their monopoly on force.
I'd argue that the violence required to maintain the status quo is less than what competing factions would exert trying to establish themselves.

While there are plenty of states doing horrible things, there are plenty that are relatively benign, and even the horrible ones are, on the historical scale, less common and more mild.
The most docile areas seem to me to be ones with a single legitimate violent actor, and pro-social systems in place to reduce the need for cooercion.

I don't think we can ever entirely get rid of the state, since at some point people will form a structure to manage or, at least document, the society they've built, and a state by any other name is still a state.
But we can wither it away if we make sure to replace it with non-coercoercive social replacements instead of leaving a vacuum like the "starve the beast" folks want.

As the smallest nit, the states monopoly on violence isn't to be the sole doer of violence, but to be the sole arbiter on the legitimacy of violence.
In a perfect system, you fighting back against the rogue cop is legitimate because the state legitimizes your use of force.
Practically, we usually only see that legitimazation happen with stand your ground laws and castle doctrine, and less police issues because the police are "special", but that's aside from the lofty theory.