In life, each person reacts different in a fight or flight mode.
Others, are more rash and dont think straight,
Others, run,
Others, are more level headed and cunning under pressure.
Point is, that us people we each have our own routines but also our own personality, thus i think it would breathe even more life if each person had some sort of predetermined personality trait, that could affect murders, for example someone cunning snd thoughtful, would think to wear gloves, and hide prints, would think to disable cameras, or toss the body to nearby wild terrain(if that was added). Others that are more rash, would do things in a haste, leaving prints, doing a sloppy job, not hiding the body etc.
This could lead, to harder to solve cases and partially fix the problem of already knowing half the population. Could also pave the way to motives, as a jealous partner for example is much more likely to execute a hasty crime.