Power
You have the power to say what killed someone, even if it's another person.
You are the driving force to catch a killer, or get an accused killer off the hook if you find evidence otherwise.
You have the power to deliver the bad news to family members. Well, actually it's more of an obligation, although you can look at it as a privilege if that makes you feel any better. It probably won't. Just remember what Uncle Ben said, "With great power comes great responsibility."
In addition to determining who shot the sheriff, you might have to step into his shoes at some point. A coroner is next in line to take over as county sheriff if he kicks the bucket. It may just be a temporary gig until the governor hires someone else, but it could give you the big chance to wear a white hat and walk around in bars.