Wasn't such the case and as said by another, it is a myth put on by Hollywood and other fictions. In the five major cattle trading towns of Abilene, Ellsworth, Witchita, Dodge City, and Caldwell there were only 45 homicides from 1870-1885. In 1869 and 1870, Abilene suffered no homicides until ironically law enforcement was put in. Witchita and Dodge City only had 5 murders in the years 1873 and 1876 respectively.

Western cities had law but had different preferences for what laws they wanted and agreed upon. Disputes were taken to Land clubs, Rancher associations, mining camps as arbitration for civil issues. The West was definitely not peaceful but not nearly as violent as films describe. Once settlement took foot, land became scarce in more populated areas. No government existed in some of these territories and ranchers took it up to themselves to provide protection by banding together in associations and claim clubs. There were formal rules drawn by the associations and would be enforced to preserve lawfulness in the land, though enforcement was by the barrel of a gun as these associations would hire gun men for enforcing the law. I'll add that these are different private enforcement agencies than the government backed Pinkerton and Wells Fargo agencies that enforced state and national law.

Eugene Hollon, Frontier Violence: Another Look

Robert Dykstra, The Cattle Towns

Robert Fletcher, Free Grass to Fences: the Montana Cattle Range Story

There was an exhibit at the Smithsonian American Art Museum called "The West as America" that made a convincing case that our perception of the "Wild West" is largely based on a mythology produced by artists (with some grains of truth sprinkled in).

I'm on mobile and I don't know how to post a link properly, but here is a URL with some information about the exhibit:

people.virginia.edu/~mmw3v/west/home.htm

I briefly studied it in a class on museum history in the context of "exhibits that piss everyone off."