Ok flash back to the 1920's. Most law enforcement was armed with revolvers that were chambered in 38 Colt, 38 S&W and 38 Spl. 38 Spl. being more powerful than the first 2 listed. A small percentage were armed with N frame revolvers in 44 Spl. and 45 Colt or 45 acp. Some especially rural areas with single action revolvers. A few relatively with the 1911 in 45 acp. Up till the 1970s the U.S. was overwhelmingly a nation of wheelgunners,
especially law enforcement.
In the post WWI period and with Prohibition organized gangs of criminals rose across the country in both rural and especially urban areas. Increasingly they were well armed to fight both each other and to fight cops. They also used motor vehicles that increased their mobility and speed. That was a novelty, meaning new. For most police depts. the use of cars was still new and most didn't have them or not many. Squad cars was still a new idea.
In the mid-west city of Chicago for example, Mayor Thompson...
"Thompson's policies, along with fears of postwar “crime waves” and “auto bandits,” led businesspeople and reformers to organize the
Chicago Crime Commission and other anticrime groups, which were modestly effective in pressing for reforms...
The automobile brought changes in police practices as well. In 1906, a mounted squad was organized to control traffic, and by 1915 police used motorcycles to chase speeders. Police began issuing traffic tickets, rather than making arrests, in the mid-1910s. The department had begun to use cars for administrative purposes by 1908, and, in the 1920s, heavily armed
detectives rode in squad cars. But communication was difficult until police began radio broadcasting in 1930. These changes, emphasizing the “war on crime,” were responses to broad public concerns. They shifted attention from controversies surrounding the police and fostered the image of police as professional, scientific crime fighters. Nevertheless, foot patrol remained widespread."
http://www.encyclopedia.chicagohistory.org/pages/983.html
The heavily armed squad cars full of detectives were armed with long guns and sub machine guns to fight gangsters when they knew where to go to get them on raids. Maybe they had 1911s sometimes. But most cops, especially beat cops, didn't have that stuff, they had revolvers in 38 Spl. if lucky.
So in the 1920s both S&W and Colt responded to a need (real or perceived, doesn't matter) for more powerful handguns to fight with. Colt chambered the 38 acp in the 1911 with a more powerful loading and called the gun the Colt Super 38. Introduced it in 1929. S&W developed a more powerful load for the 38 Spl., placed it in a larger frame for a 44, and called it the 38/44 Heavy Duty with fixed sights for police work and the 38/44 Outdoorsman for hunting with adjustable sights introduced that in 1930. Both companies advertised that the rounds would penetrate auto bodies. Both companies responded to a new opening in the market for more powerful handguns.
Did it matter that the more powerful rounds more reliably penetrated into the vehicle and through the occupants of the vehicles? To the cops it did. Even if just the idea of it.
It's worth noting though that the majority of law enforcement never did adopt semiautomatic handguns till long after the second world war. Neither did they transition to the more powerful 38/44 round or the 357 Magnum though the latter did become popular with many police after the war. Most depts. never left the 38 Spl. till the transition to semis. But it was the special squads of "detectives" and the FBI, etc that did want and use more powerful handguns and more armament in general.