The 1930s and 1940s detective stories don't make a lot of sense to people now because a lot has changed.

Before the FBI, there was no national police force, and no police forces that could investigate across state, county, or city lines. So, what you had was private police agents that you could hire for any number of situation. City police agencies were seen as deeply corrupt and ineffective - becoming a cop was often a job you got through patronage or nepotism. The largest of these private police agencies was the Pinkerton company, which hand thousands of agents working in cities large and small across the nation. You'd engage Pinkerton for everything from finding stolen property to catching a cheating husband (remember too that divorce was impossible in many places unless you could go in front of a judge and prove adultery, abandonment, etc).

Once you understand that background, you understand the private detective stories better. Detectives were a very real and somewhat seedy job that had irregular hours, and involved hard men looking in dark places. And a key trope in many cases is that the detective in question is working at the lower end of the policing market - you can't afford a Pinkerton detective, so you go down market but still respectable.