One Case At A Time

In real crime solving, a case can sometimes take months or years to wrap up. Yet in TV drama, a case is opened and closed within days - never more time than can be shown in a single a episode. Further - and this is what this trope is about - the protagonist is only ever investigating one case at a time. While real detectives likely have several concurrent cases, in TV drama detectives are rarely shown to investigate more than one crime at a time. The detectives will focus every waking moment/work hour on that one case until it gets solved, and will never shelve it  even for a few hours to investigate some other crime in the meantime. If a detective character is shown or said to be working on a different case, it will nearly always be connected and hold a vital clue to the main case. Otherwise, in shows that have A plots and B plots, the B plots are usually something related to the detective character's personal life rather than the case-of-the-week.

One big reason for this is the Law of Conservation of Detail. In other words, we only see the detective on that particular case because that's what the story is about, so this apparent single-mindedness is only apparent. We don't see every toilet break, meal, or sleep cycle (presumably the detective continues to meet their bodily needs unless otherwise specified). The audience will hear that the sleuth went to see someone later the same day or the next morning or whatever, and this may be visually indicated with editing cuts, a shot of the new location, and/or a music cue that suggests the passage of time.

It's also true that Cop Shows and detective fiction lend themselves to the Stand Alone Episode structure; each episode/novel/short story is about a particular case, and most of the participants are often never heard from again once the case is solved. This is supported by real-life methods of organization such as the case file (for an individual crime event or victim) and the courtroom trial (of a particular culprit for one or more discrete crimes).

From the creators' point of view, it is easier to attract new viewers if those newcomers don't have to be up to speed on a multi-episode Story Arc. This desire to attract and grow an audience used to weigh more heavily than considerations of realism. Thus, a string of one-offs was standard for cop and detective dramas until the advent of Hill Street Blues in the 1980s. Since that show had success with audiences and critics, shows with multiple plot lines in each installment and multi-episode story arcs have become much more common, and shows with this structure somewhat less so.

As this is an Omnipresent Trope, No Examples, Please.