Actually, the idea that cops did not carry autos in the early part of the 20th century is a misnomer.
Like everybody else, THEY DID!!!!
Colt 1911s, Savage .32s and Browning pattern .38 and .380 autos were very popular well into the 20s and 30s.
For years, the NYPD did not even offer holsters. Officers carried their .32 autos and .32 revolvers in coat pockets.
What happened was two fold.
Number one, there were a lot of accidents with the striker fired single action autos.
Number two, the .32 and other rounds were found to be woefully inadequate when it comes to stopping power, and this left the 1911 and the High Power along with the occassional Luger or rare Walther p-38 the only viable semi autos for LE use for years to come.
Remember, most agencies would not allow or issue a foriegn made gun back then. Still,, many cops carreid Colts. G Gordon Liddy recalls his uncle, an FBI agent packing a Colt .38 Super. Frank Hamer used the same type of gun to take down Bonnie and Clyde.....
There is another factor too, that comes into play...
Notice that up till Cooper's era, most men who packed a 1911 packed it hammer down on a live round, sometimes half cocked.
Considering that a double action revolver is faster to draw and fire than a single action auto that is to be THUMB COCKED, the DA revolver caught on like wildfire by the forties and fifties. Also, by then, experts like Keith and Jordan were weiging in on the side of the wheelgun.
Outside of soldiers in the field, pretty much nobody was packing cocked and locked prior to Coopers ascendancy. Elmer Keith recommended it in his book Sixguns in the fifties, and people thought he was crazy.....
Something else to consider. Not every police officer is as into guns as say you or I. It was even WORSE back then in the days before "Officer Survival" became a tag word.
Most older cops (who were not into guns) would be asked why they carried a revolver instead of a military auto and instead of admitting that they didn't know would say, "Autos are jammamatics."
(You still encounter this attitude with older officers vis a vis giving bad advice to the public. I think we all know some crusy old timer who was told by some wrong headed but well meaning officer that if you shoot somebody drag them into the house and plant a knife in their hand. That is tampering with evidence and would easily get you imprisoned in this day and age.)
Seeing as how the only guns that many of them ever encountered which were autos were cheesy saturday night special types, they bought into that myth.
The reality is the autoloader (especially Colt 1911) had proven itself for reliability as early as WWI.
As for agencies issueing them, El Monte PD issued Colt .45 autos way back in the sixties according to Joseph Wambaugh.
Other agencies large and small have issued or allowed 1911s and high powers way back before the new wave of police autos arrived in the mid seventies and early 80s.
In David Morrell's novel "First Blood" Sheriff Teasle is packing a high power. It takes place in Kentucky....Many officers I know who were on duty way back in the sixties and seventies in Kentucky also packed High Powers.
So what it boils down to is this. For a brief period of time, autoloaders were popular with police at the turn of the century through the roaring 20s.
Then the DA revolver became fashionable and in time the autoloader was pretty much verboten to rank and file cops on big departments.
Not knowing why, many officers just assumed there was a valid reason.
For decades it stayed that way as LE brass tends to be hide bound and reactionary.
Personally, I think the LE world has gone in the wrong direction today. I can think of a half a dozen shooting incidents over the past few years where honest officers were castigated (by people who don't understand terminal ballistics) for shooting suspects multiple times. It probably would have not happened that way, had they been packing wheelguns in effective calibers.
I really think that with a big bore or magnum, the fight would have ended in one or two rounds and saved these officers and their departments a lot of grief....