J, I think you’re right. Many mystery stories feature Protagonists whose persistence is a primary feature. Indeed, it’s that resolute nature which is key to them solving the case.
There are exceptions, of course. You mention the TV series “Wallender” as an example. One could argue that Jake Gittes in Chinatown has an arc in shifting from a cynical loner to someone who actually cares about someone else, although by the end of the story, he has even more reason to be cynical (“Forget it, Jake. It’s Chinatown.”)
Arc. No arc. Whatever serves the story best.