I think I personally have had less fun with murder investigations since the tutorial. Overall, I loved the idea of someone leaving a note that led to a case. But all jobs after, for me at least, they have all been reported by the police scanner and immediately the place is in lock down. By the time I get there, the cops are almost at the location and searching the crime scene undisturbed is near impossible.
Some people even sleep till murder cases happen. So you may lose even more time due to the fast forwarding.
Suggestion
I would like more methods then the police scanner and random luck to stumble on a murder. Having someone call the detective could be great incentive to buy a phone or maybe a payphone rings and you answer it to get a tip (which could be ominous and creepy). Maybe the homeless people can lead you to a building that has a case waiting to be found for some cash. Definitely could see some other ideas coming in.
Beyond this, my second suggestion is if the police scanner goes off then maybe wake up the player automatically and stop the wait time? They could just go back to sleep if they don't care and it could stop you missing vital minutes due to fast forwarding while while waiting/sleeping.
