There was never a tradition of the police in the eastern US carrying large caliber handguns except for state police. One imagines they somehow saw themselves as different. Likewise by no means did anarchists, nationalists and terrorists necessarily carry large bore revolvers. The shots that started WWI supposedly came from a .32 automatic fired by a man who had never fired a gun before
While this is certainly true, what I was speaking of was the perception and attitudes of the general people. In the US good guys carried big guns, and were often lone hero types. In Europe, rather the opposite. This was not any kind of hard and fast rule, and actually seldom accurately reflected reality. It was just how many people, particularly those not actually in police work often felt.
But it was the common attitude, and reflected often in popular fiction. Not by any means the sole cause, or even necessarily the most important one, but before, and during the first half of the 20th century, these attitudes often were a significant factor, particularly in Europe.
Note also the era. In the early years of the 20th century, particularly in urban areas, the horse, as the primary means of transportation was being replaced. Trains, carriages, streetcars and simple walking in cities, with the indiviual rider declining. The advent of the motor car kicked the change into high gear. Lawmen in urban areas dealt less and less with the need to stop a horse mounted man. Carrying big bore guns capable of stopping a horse simply weren't needed.
And as automobiles became more common, and more commonly used in crime, note the change from the .32s to .38s, and eventually the .357 Magnum, in the US.
European police simply didn't face the same kind of situation as the US did, with our gangster era, prohibition, and the "motor bandits". For them, the small caliber pistols were enough, for a long time.