@FrenzyMode
As was already said, trigger discipline in the present-day view is pretty recent. Just look at the holster Forgotten Weapons did a video on the other day; that thing needed you to violate modern safety rules every time you drew from it.
Realistically, it's a Wild West setting, and they're single-action guns. Looking at it from the perspective of someone in the time period, if the hammer's not cocked, what's going to happen? it simply wasn't something they worried about.
@anon763 to add to this: most gun savvy people in the old west only ever loaded 5 of a revolvers 6 chambers (or one less of whatever the maximum was) and set the gun on the empty chamber to prevent accidental discharge.