If the BD king doesn’t have investigative abilities, why would the get hung for not providing info? You wouldn’t hang a knight for not having and leads, or a physician for not having any leads. If they DO have leads, then you’d be more likely to hang them, since the only way the BD king would have these results is from someone else.
The only reason he gets hung so easily is because everyone knows he has leads. Removing it would lengthen their lifespan, not shorten it.