Of course, we must not forget that the 1911 has been around........oh, since about.........1911 and law enforcement agencies agencies have overwhelmingly REJECTED it because it's too complicated and has too many safeties for the average cop to cope with.
While there is some truth to this, I think you are adjusting facts to fit your ideas and not taking into account some rather important factors.
Yes, the 1911 was complicated and a bit much for most cops, in 1920....
Not all the soldiers were comfortable with them, either. Patton himself disliked the 1911, because he had an accidental discharge with one, and never trusted them afterwards.
I think one of, if not the primary reason the police resisted semi auto pistols (In general) for so long was simply the cost. And, the cost involves more than just the purchase price of the pistols. You also have to figure in the cost of training your officers on the new weapon.
I don't have the prices from the 30s or 50s, but I do have the MSRP prices from the mid 70s, and in 1974 a S&W Model 10 was $96. A Colt Govt model (1911A1) was $134.50 and a S&W Model 59, (double stack DA 9mm) was $150.
Remember that the guns bought and issued by most police departments was a decision made by the various chiefs of police, or the mayor or some other bureaucrat, NOT the line officers.
Do note that for many, many years police officers were forbidden the use of magnum ammunition (when they had magnum revolvers) and were also forbidden hollow point ammunition.
Generations of cops lived under those restrictions, because the people running the depts demanded it.
Also, if you want to look at things with a broad enough lens, the cops going to DA semi autos didn't happen until the 80s while the DA semi auto service pistol first showed up about 1938. SO, nearly 50 years of cops sticking with revolvers over DA semi autos, and SA semis were first adopted by a couple of states about 1970.