I think one of the most important parts of the detective feeling is investigating about the motive. What lead the person to commit the crime. And I think is not very well covered.
We should have a list of different motives and be able to connect clues like mails or notes as proof of that motive. And it should be mandatory when closing a case.
Also, these motives could help us predict future victims. We could also have crazy lunatic killers that doesn't have motives and their victims are unrelated to each other. Those type of killer would make the case even harder.