Sure, but there is really no shortage of known unsolved crimes.
> The police does not put out press releases repeatedly with 'we got no leads'.
They do, in all the cases I listed they've asked the public for help for years. Certainly they don't do that for crimes they don't know occurred, but there is no shortage of known crimes that are very publicly unsolved.
For that matter, there are also a whole lot of missing person bulletins soliciting information from the public. Many of them might be murder victims, but it isn't known whether they are really alive or dead, let alone murdered. The public is nonetheless asked for information.