As a reader I've given up on the idea that there's anything that can "never work." I've read novellas without plot. I've read novels told from the point of view of a buggy not-actually-self-aware computer program, and while that didn't quite work, I did make it through the novel and it did receive good reviews.
As an author, I've found that the answer to such questions is to go try it and see how it works for you. If you succeed, you know the answer is yes. If you don't, you know you couldn't do it then.
That said, what you propose sounds difficult.
There are definitely crime procedurals with a mostly sociopathic main character (Consider the Richard Stark Parker novels as an example).