Think about it. In the early 20th century, the time that this poster is referring to, there were no Glocks, Rugers, or S&W semi-automatics. Europeans preferred the semi-auto because it could be concealed easily, and were quite satisfied with the .25 and .32 ACP. The 9mm Luger was considered a military caliber. The United States had settled on the 1911 Colt, but they were still pretty rare.
The revolver held 6 rounds, the new Colt 7. The powers that be didn't trust the new-fangled autos, and everybody knew that the .38 was enough for a policeman.
As for the trigger and city lawyers, that's a relatively new deviant practice, suing for any and everything. In the early 1900's, through the 1960s, if you ran when a cop told you to stop, and you ended up shot during a scuffle, that was your problem. People still believed that wrong-doers deserved what they got.
The Texas Rangers were a little more progressive, with the 1911, the Mauser C96, and the Luger being used by men who decided that they were the way to go. It wasn't like they were issued pistols, you bought your own. Most police departments were that way, too. Revolvers were a way of life with the veteran officers, and the rookies were pointed in their direction.
I believe that the first large department to switch to semi-autos was the Iowa State Police, with the S&W Model 39, and one of the last was NYPD.
Looking at this, I believe that America with it's firearms conservatism, was what kept the revolver in officers holsters, and the .38 Special in the weapons cylinders.