The fundamental problem with this line of thinking is that a society in which mere disagreement can be met with deadly force is no different than a society in which the strongest (as in, the quickest to draw) rules. You can't claim to be an open society if you don't allow perceived and actual slights to exist, and we've all seen people getting shot on highways for cutting someone off.
The "Wild west" is
kind of a myth though. Gun ownership was regulated in frontier territories and gun battles were rare.
The linked Smithsonian article has a lot more facts about gun control in the Old West. It's just terrible that much of our understanding of the past is still driven by John Wayne movies instead of the actual accounts of folks who lived in those times.