I started shooting in CAS matches over 10 years ago so I have the advantage of having heard many questions about SASS asked many times. I've also heard the answers given by various members of the Wild Bunch.
Having persuaded many folks to give SASS a try, I'll give you my version of the answer.
When we were growing up our heros were the movie and tv cowboys. I grew up with horses and western tack. I dreamed of Colts and Winchesters. None of my cowboy heros normally used double action pistols. They didn't shoot bolt action rifles. SASS has a historical side but it is a fantasy game with safety and fun the main components. SASS does allow some double action pocket pistols in side matches or as a staged, match provided gun. WASA and NCOWS have different rules if you want to play by a different set than SASS. They allow you to use historical double action or even some semi-auto pistols as main match guns. Also there are many unaffilliated CAS clubs shooting by their own rules. If you shoot with the Cherokee Cowboys, it'll be by SASS rules.