I wonder what would have happened if Homicide- life on the (killing) street was never made. Exept Munch not appearing on every damn show known to man. But it wouldn't stop mystery solving shows in general.
The problem is that the mystery format is so good. You have somebody that need to contact people, interact with them and so on. And it is interactive for the audience, they can try figuring out whodunnit.
You can't make the same thing in an doctor show for example, it require some medical background to figure out the more complicated things and the easy stuff, well how hard is it to figure out that the big bleading wound in the chest is bad for you. (As far as I can tell, the good medical dramas are character driven drama.)
Take another cool profession, pilots. You can't really pull of an interesting show featuring pilots. Police, it's easy.