He might not be the sharpest mind in St. Mary Mead, but Inspector Slack certainly does his fair share of mystery-solving as a police officer. On a serious poin

He might not be the sharpest mind in St. Mary Mead, but Inspector Slack certainly does his fair share of mystery-solving as a police officer. On a serious point though, I think there is some value in purely investigative work by the police even when there's no prospect of a successful prosecution. Unusual cases might lead to better insights into things that affect many more people: revealing well-hidden criminal gangs for instance. Even if the police can't pin the guilt on a specific suspect or accidental cause, the result of an investigation might simply be better public awareness of a risk, which is a good thing.