Fame
Better watch out. People don't like their coroners to be famous.
Dr. Thomas T. Noguchi, once known as the "Coroner to the Stars" got in big trouble after he bragged to the press that William Holden and Natalie Wood had a few glasses too many before they met their untimely demise.
Hollywood big shots tried to keep him from talking to the press when it came time to announcing John Belushi's drug problem as the cause of his death, but he didn't comply. Soon after, Noguchi was brandished in the press for being lousy at his job and "forced into early retirement." So yeah, it's probably better to keep things on the down-low when it comes to working with the deceased.