My 2 cents as an Army vet, LEO, and FI:
The police dept. adopted the revolver at a time that autos were known to jam often. The only exception would be the 1911, but even the Armed Forces didn't want those carried cocked and locked (I've seen ND's with 1911 in the Army & the PD). So for safety and reliability, the revolver was king.
Then, the DA auto was invented. It was safer than the 1911, and came in 9mm, which held alot of rounds. When criminals started using hi-cap 9mm's on Police and each other, the Police wanted to at least be able to match them. 4 CHP troopers were gunned down in Newhall, CA during the early 1970's, and the slow reloading of the revolver was cited as one factor. A NJ State Trooper was gunned down by 2 Left-Wing terrorists on a traffic stop in the early 1980's. His revolver ran dry, but their 9mm pistol (Hi-power(s?) did not.
Since, autos had became more reliable and safe, and officers felt a lack of capacity was a problem- the 9mm got the nod over DA .45acp autos like the S&W and Sig. Plus at the time(mid-1980's), 9mm pistols could be compact, while the .45acp DA autos were still pretty big and heavy.
After Miami, the wounding effect of 9mm was called into question, but the need for plenty of ammo in the gun and on the belt was not. So, the .40 was invented. If wounding had been the only factor, the Sig P220 probably would have got the nod from the FBI.
I started my LEO career with an issue M-10 .38spl., but I quickly bought a then new G-17 for the extra rounds and the 9mm with JHP had a better street rep than the .38spl. My Dept went to the P228 9mm with a "safe" 12++ DAO trigger pull. (we still had a few ND's
).
Now, we have P220R's and we like them. They are a bit too big for plainclothes/off-duty IMHO. I know from OIS's that 147 9mm Golddots and .45ACP RangerT works with good placement(two DRT's, respectfully). FWIW
The .45acp seems to be becoming more popular in Law Enforcement. I think the increase in Meth-Heads and cocaine users taking considerable punishment before dropping has been behind this trend.