I suspect that one reason the police never went wholeheartedly for big cartridges was, aside from the fact that they are harder to shoot, they don't work all that much better, contrary to everyone's opinions. And when I say harder to shoot, I mean even for experienced shooters. Some police agency used the .41 magnum but it didn't last long.
You may also recall that when Theodore Roosevelt chose a .32 Colt for the New York police, it was after it had been tested on animal carcasses, just as the .45 ACP was done later on. Before that, I understand there had been no standard handgun. They did, however, eventually switch to the .38 Special. I don't think they ever used the .38 Long Colt. And by the way, whether or not you believe there was ever a .45 Long Colt, I suspect it was only natural to use the term because of all the other cartridges that had a long and short version, both Colt and S&W.
However, some agencies, mostly state police or highway patrols, did apparently use large frame revolvers, though not necessarily big bore. Interesting to speculate on why that was the case. Texas Rangers on the other hand were exceptional in using .45 autos sometimes and I am certain some carried them cocked and locked even in the 1950s, before both automatics in general and the .45 auto were considered satisfactory for police service. The Illinois State Police, I believe it was, were trendsetters in adopting the Model 39 S&W pistol, used with a crossdraw holster, I think. Wonder what they use now?