Yeah, not least because Stetsons were actually relatively expensive. Which doesn't mean that a cowboy or other Western figure might not have considered it worth paying for, but there were many cheaper alternatives.

"Contrary to popular belief, it was the bowler and not the cowboy hat that was the most popular in the American West, prompting Lucius Beebe to call it "the hat that won the West."" - quote from Wikipedia, but footnoted to a 1957 article by Beebe in "The Deseret News":

"A few years ago a writer was engaged in preparing for book publication a pictorial history of the Old West. He examined literally thousands upon thousands of contemporary illustrations, especially photographs, and after a time he became haunted by what at first seemed a recurrent and indefinable but ever present anachronism. At length it dawned upon him that a formidably large proportion of the population of the Old West, the Wild West, the West of everybody but Frederic Remington and his imitators were wearing derby hats and not Stetsons."

(Came across that when trying to look up my vague sense that the "ten gallon" style made by Stetson is actually from later, but I wasn't sure what "later" might be. I was going to reply to you that you can also in some cases make a guess as to time period, by the hat style. Which is not to refute the idea that "the cowboy hat" became popular and widespread -- it had a lot of practical features, it became popular for a reason. Just that, as you and I are both agreeing, that doesn't mean other types of hats weren't found in the Old West, or even "typical" of the Old West.)