You know, thats one thing I have always wondered about, why for the most part, its uncommon out here on the west coast for city/county's to use paddy wagons, like they do on the east coast.
The biggest reason you see a tradition of paddy wagons in the East is driven by the way the US grew up. There has always been a higher concentration of population East of the Mississippi River (including St. Louis, which was the biggest city in "The West" and served as the 'last outpost of civilization' when the settlement of the western frontier began). The cities in the East were built up (tall buildings) rather than out (sprawl) because there were so many people to pack into small (geographically speaking) areas.
As a result, most of the cities in the East had huge populations living in physically small areas. Police could and did patrol and keep the peace on foot. When an arrest was necessary, however, the foot patrol officer could not effectively transport a prisoner or two to the station. So, a wagon was employed to circulate among the foot patrol beats for the purpose of picking up arrestees and hauling them to the station.
Contrast that to the wild, wild West where land was far more plentiful than people. Police could not walk beats. So, law enforcement in the West grew up more dependent on lone patrol officers having all the tools they needed at hand, including a means of moving prisoners themselves. There were no circulating paddy wagons to transport prisoners, so those new-fangled patrol cars were equipped with onboard prisoner detention accomodations. Originally, sturdy loops on the floors to attach shackle chains; later, what we call "cages" or "prisoner shields" separating the front seat from the 'customer service' area.
Notice also that Denver, Los Angeles, and San Francisco became very large cities early in the growth of the Western U.S. They had downtown areas that grew "up" with dense urban populations, similar to the Eastern cities. Foot patrols and paddy wagons were employed in those locales, much like the East. In later years, other population centers like Wichita and Phoenix utilized paddy wagons.
But the use of paddy wagons has always been dictated by population density and the presence or absence of foot patrolling.