What might be even more fundamental is that the detective genre is about the establishment (the detective, professional or freelance) taking on the forces of chaos and disorder (crime, social disruption), whereas in fanfic the focus is normally on those forces of chaos, ie; outside the establishment.
Assigned reading for tonight, any Raymond Chandler novel. Phillip Marlowe, the detective, once worked for a DA's office. These days, as a P.I. he still has enough friends on the force he *might* not get his liscense yanked just because he won't break his client's confidentiality: but he'll probably need help leaving his jail cell because his kneecaps have been banged up as someone's idea of fun. Bay City, where he's sometimes had to go, the police would shoot him if he pursued some investigations too far. In short, Marlowe deals in chaos. He tries to make things a little less chaotic for his client, and that means a lot of... Beautiful Suffering(?) in the process. He usually goes up against corrupt officials, organized crime, and rich people who can afford bodyguards. This sounds very much like the Federation.
Hmm. I think I may end up trying to write my own dectective Blake's 7 story.