Perhaps because it's not a myth at all.
The West WAS definitely wild in the sense that there was little law enforcement other than what a person enforced him/herself. However, many people were brought up on Bible verses memorized through daily readings and repetitions. They often also learned how to read and write using biblical stories and texts because, even though there were few other books available, a family Bible was generally to be found in every household, listing names and dates of births, baptisms, marriages, and deaths through many generations.
Most folks were raised to have very strict moral underpinnings which ruled their entire lives. They had a code of honor which would allow only fair play in both war and peace. Because of this, bad people often succeeded in their nefarious schemes, and those with no sense of right and wrong often would only be punished for their misdeeds if caught and tried for their crimes "on the ground where they committed them." This is where lynchings came from. It wasn't so much mob behavior as community displeasure in immoral or bad acts, and the sure and certain community knowledge that, if THEY didn't act to stop the evil-doers, no one would. There simply wasn't anyone else available to do so.