since the 1850s or so, there have been a number of double action revolvers that came and went as it seemed they werent all that popular for one reason or another, and it seems single actions were common throughout the 1910s
Eh, the double action began to gain in popularity in this country in the 1880s with the S&W (1st model double action .44) and Colt (Frontier) offerings. Of course, the top break design, while very fast to reload, isn't terribly strong. Meanwhile, the Colt, though able to fire more powerful rounds, still had to be loaded like a single action. But by the turn of the century, viable swing-out cylinder DA revolvers were being produced. They quickly became the dominant law enforcement sidearm, and remained so basically until the mid-1980s. The S&W revolver really hasn't changed much since the 1903 hand ejector, either.
Europeans, of course, favored double actions long before we did. But they also typically chambered much less powerful cartridges, and weren't usually subjected to the kind of abuse guns endured on the American frontier. So a more complex system with smaller moving parts wasn't as taxed, and the much more established landscape of Europe, civilization-wise, meant that having the guin serviced wasn't so burdensome. Can you imagine having your one and only revolver fail on you hundreds of miles from the nearest gunsmith, when you're travelling in a carriage or cart moving at an average speed less than a typical walking pace?
This, of course, is why the shotgun was really the gun that won the west. It was simple, robust, versatile and stone axe reliable. The lever action rifle and single action revolver got the hollywood glamour, but the shotgun was what really got it done back then.