Howdy
A few things to think about:
When the Civil War ended in 1865, the American government had thousands of 36 and 44 caliber Cap & Ball revolvers in inventory. Smith and Wesson dominated the cartridge revolver industry until about 1870 because of a patent they controlled. Up until that time, the only cartridge revolvers manufactured in the USA were those made by S&W, however they were all small pocket pistol type revolvers. However when the patent expired S&W produced the first of their large 44 caliber Top Break revolvers, a model that eventually became known as the American Model. The Army ordered 1000 of these new revolvers.
By 1873, Colt was producing the Single Action Army, the iconic 'cowboy revolver'. The Army purchased 8000 in 1873, and more later. Not to be left out of the military market, S&W developed a 45 caliber Top Break revolver named the Schofield Model, and sold about 8000 of them to the Army.
What this meant was that all those Cap & Ball revolvers the Army had in inventory were suddenly obsolete, and the government began selling them off cheap.
Most cowboys were relatively young men, many were Southerners displaced by the Civil War. While they might not be able to afford the latest and greatest products of Colt and S&W, many of them could afford to buy surplus C&B revolvers, and many of them did.
In 1873 Winchester produced their Model 1873 lever action rifle, which was chambered for a new cartridge known as the 44-40 cartridge. By 1878 Colt was chambering the Single Action Army for 44-40, so now there was the opportunity for somebody with some cash to be able to afford a cartridge revolver and a fast shooting lever action rifle, both chambered for the same cartridge. And many did. My reprint of the 1875 Winchester Catalog, the first year the Model 1873 was cataloged, shows a standard Model 1873 rifle sold for $40 and a Carbine sold for $38. A lot of money back then, but by 1900, which is often considered the end of the Frontier in the West, Winchester had sold over 500,000 Model 1873 rifles. In the same time period Colt sold over 200,000 Single Action Army revolvers. Clearly, not all of these guns made it out west, but a significant percentage must have. And that was just Colt and Winchester.
I find it tough to believe that pistol usage was that widespread given the cost of the guns, ammo and overall capabilities of the side arms of the day.
I am not sure what the OP meant by 'overall capabilities of the side arms of the day', but I can assure you a Single Action Army revolver loaded with 45 Colt cartridges was a very powerful revolver. 45 Colt was in fact the most powerful factory loaded ammunition available until 1935 with the advent of the 357 Magnum.
This is a photo of a working cowboy taken circa 1887. Notice the pistol on his hip and the rifle in the scabbard.
This is Commodore Perry Owens. No he was not a sailor, that is the name his mother gave him. Perry Owens was a well known gujnfighter and lawman in the Arizona territory in the 1880s. Notice his unusual holster and gun belt, with rifle cartridges for his single shot rifle at top near his hand and revolver cartridges below.
A couple of Texas Rangers.
This is a staged photograph taken in a photography studio. The backdrop is obvious. There are many studio photographs like this from the 19th Century. Sometimes Easterners would dress up in cowboy clothes for these photos. However this young man looks much too at ease to me to be anything other than a real, if very young, cowboy with a revolver in a cross draw holster on his hip.
And let's not forget there were a lot of black cowboys too. This fellow has a Colt Cap & Ball revolver tucked into his waistband.