I think it's easy for industry people to lose sight of how important the central mystery is to a good detective drama. The temptation is always to believe that it's the character of the detective that drives the narrative. Hence the crude attempts to make the crimes 'personal' by killing off relatives, friends and, I'm looking at you Inspector Lynley, the odd girlfriend or fiancé. This represents at best a failure of nerve by the production team and at worse a lack of understanding of the genre they are working in. Look at the classic detectives, Morse, Frost, Holmes and you'll find that they have character traits not character arcs.
Morse was the same grumpy beer drinking, opera loving snob in his last episode as he was in his first. This is because the single most interesting thing about Morse was that he was a police detective, the opera and the expensive education were interesting only because they contrasted with his job. Likewise without their careers in detection Frost would just be an opinionated northerner in a pork-pie hat, Dalgliesh a failed poet and Holmes, well god knows what Holmes would be - dead probably.
A good TV detective is distinctive, charismatic and three dimensional but a writer must never forget that at the heart of every mystery must be a good murder.