The saloons were originally collegium, idk what you are trying to correct here.
Deadwood had a retheme to the west but it wasn’t really a western or a cowboy show.
All you have to do it watch it. It does not have anything g to do with Rome. Again, the creator pitched it as taking place in Rome during the reign of Nero. Because the show is about cops in a place with no laws, not Rome.
My dude I’m not going to argue with you about settled fact. In fact I’m not disagreeing with you except in saying that deadwood isn’t a show about cowboys.