Ok, very over-simplified, but in a time when technology can do whatever the writers need it to do in order to tell a story, it doesn't leave much wiggle room for proper cop-show elements.
Have you ever seen, like, one episode of CSI?
Of course, it's kind of hard to miss.
But seeing what the writers make happen now, add all of Trek tech and technobabble onto that and it steals the suspense away from the crime and hunt for the criminal.
Then there would be questions such as, where would it be set? It couldn't be on Earth as it is paradise and having a weekly murder would take away from that. A station that had major crime of a frequent basis would raise the question of why people would continue to go there. A starship zipping from crime scene to crime scene would have the problem of travel time and exactly how severe a crime would need to be to warrant their involvement. A colony or alien world would have to be the answer, but could it be a Star Trek series if they were stuck on a single planet?
Just some thoughts.