I posted this in the "Faux Life" forum, but it's relevant here so I'm bringing this here:
I didn't really watch much of Murder, She Wrote, but my mother and my grandmother (who have both sadly passed) loved the show. So I'm intrigued by the Jessica Fletcher murder theory, so much so I wrote a short fic where she gets arrested.
I also found this article from the Waterford Whisperer out of Ireland:
I guess Jessica is too easy to figure out.
On a more serious note, from what I understand about the show, the reason why I think the murder rate is so high in Cabot Cove and whenever Jessica Fletcher is around has a short and long answer. The short answer is- as has been pointed out before- without a murder, there's no show. I mean, it's not "Kidnapping, She Wrote" or "Robbery, She Wrote", or "Parking Violations, She Wrote".
(Though I guess "Speeding Tickets, She Wrote" could have been a fun series...but I digress)
The long answer is that I believe Murder, She Wrote is supposed to be an '80s version of the classic early 20th century detective tale where there's a huge dinner party and either the host of that party winds up dead or one of the guests. Writing these kinds of stories requires the crimes to have a very personal connection, because the mystery part of the story just doesn't work unless the reader tries to figure out who's got the greatest motivation to commit the murder.
Which is pretty much how the cases on Murder, She Wrote worked. We may not have had a literal dinner party in every episode, but the style was still very much the same- Jessica encounters a group of people, one of those people wind up dead, and the murderer is the one who had the greatest reason to want that person dead. I may be wrong about this, but I'm not sure Jessica solved many of her crimes via great forensic work or even via simple detective work, i.e. clearing someone simply because they had a reasonable alibi. I'm sure Jessica solved her crimes by showing that the murderer had the most personal connection to the crime, either via motive or knowing something about the victim that only the victim could know.
Which means, personally, the idea that Jessica Fletcher is a serial killer fails the Occam's Razor test. If she was a serial killer, she'd likely need a lot of help to facilitate the murders, planting evidence to not just throw the police off her trail, but to also frame someone else for the murder and make it so believable that the framed party committed the crime that others are convinced they did it. Oh, and do it so well that the people who were framed would actually get convicted of their crimes, which would likely need the assistance of the prosecutors- perhaps all the way up to the Maine Attorney General.
Ultimately, I just look at this series as a product of its time. In the '60s and '70s, you had the end of the Hays Code and the Comics Code, which meant writers could start exploring darker material- so many did. The "pure mystery" featuring the "wholesome detective hero/heroine" where the story was a literal puzzle and the hero stood tall amidst an adoring crowd at the end would give way to the detective who was so affected by the realities of their job that, while they'd be great at it, their lives were still a complete mess as a result (which would eventually give way to the "almost villainous" crime fighters we see now). Stories focused less on figuring out who committed the crimes and started to focus more on the how and why the crimes were committed. The idea that the hero had to be entirely good and the villain entirely bad eventually fell by the wayside, leading to where we are now where lots of shows blur the lines between who is evil and who is good.
In short, it's weird to think about considering how recent the show is, but Murder, She Wrote was a relic, a throwback to a different time. A lot of the inconsistencies- like Cabot Cove's insane murder rate- can be chalked up to the show's format, as I'm sure the creators wanted a show that was "wholesome" and "morally upright", which meant they couldn't place it in a big city and they couldn't have a heroine who was "too dark". It does make me wonder, in this deluge of detective shows where the cops are practically villains themselves, if we're long overdue for a series like Murder, She Wrote where we just get a straight-up "whodunit" with an actually heroic detective putting away actual villains, maybe with that hero struggling but showing they can overcome their struggles.
It may just be too long since we've had an actual hero on our screens.