A good complex question.
First, before the 1980s the U.S. was a nation of revolver shooters. Among those who shot handguns the wheelgun dominated. Semis were a smaller section of the market. Small back up semis were arguably more popular than bigger semis till late into the post war period.
Colt was the only American manufacturer to produce semis in a military caliber and that was the 1911A1 in 45 acp and 38 Super. The American public in general considered the 1911 a military sidearm. The gun in either caliber did not see widespread use in law enforcement in the U.S. That market was dominated by revolvers.
The pistol that most impressed the U.S. Army coming out of the war was the Walther P-38. So impressed were they that in 1946 when they drew up plans for a sidearm to replace the 1911 it was essentially for a gun based on features of the P-38. DA/SA guns began to be seen as much safer and modern.
Colt was the first American manufacturer to chamber a pistol in 9mm and that was with the Commander in 1948.
S&W produced and sold it's first semi-auto pistol in a military caliber in 1954. It had many of the desirable features of the P-38. Slide mounted safety/decocker, da/sa, 9mm, etc.
Other than a few war trophys few BHPs had been seen in the U.S. till the post war period.
In 1954 FN began importing the BHP into the U.S. in limited numbers.
During the 1950s and 60s war surplus rifles and handguns flooded the U.S. market. P-38s, Lugers, fine Spanish pistols, etc. most in 9mm and many times cheaper than the U.S. made products. Guns from Argentina, and Brazil, many based on the 1911 in 45 acp, also made a showing. Many of these were perfectly fine and excellent guns. If you wanted a 9mm you could get one for less than a weeks wages, often for less than the weekly grocery bill. These guns sold like hotcakes!
The BHP sold slowly but well over the years.
I'll skip a few things here, some already mentioned.
By the time the transition in law enforcement began in earnest in the 1980s the accepted doctrine on gunhandling for leos was that single action handguns were passe. The safest way and preferred way for law enforcement was da/sa, the long heavy first shot trigger pull, followed by easier single action trigger pulls, with a slide mounted decocker/safety. Firearms instructors taught this and it was almost universally accepted. The idea that a single action pistol like the 1911 or bhp was fit for police work only in elite units began to take hold. S&W semis ruled the roost till the M9 was adopted by the U.S. military than that gun began showing up in large numbers in cops holsters. The Sig too after a bit.
In a few years though the doctrine that weighed against the 1911 and the BHP, so solid, professional and sacrosanct, was overturned by the arrival of Glocks.
These guns don't need much. Improve on the trigger, better sights when needed, a better thumb safety. Over the decades there have been good smiths who can provide the features that are desired. FN itself never responded to the market as well as it could have I think. But their contracts have always been heavy on the military side.
tipoc
I think of it as a built-in safety of sorts. Someone who is either very young or very old, or simply weak for whatever reason, couldn't rack the slide to save their lives. Or take mine.