Nope. Holmes wasn’t a police detective, but he certainly was a detective, and hardly an amateur.
Now, let me tell you about My Three Sons…
Stranger
While I love the show, Mac wasn’t a cop, he was (the) Police Commissioner. He wasn’t in the chain of command. Enright (and later Dimaggio (no relation)) was a detective, though, and was always at Mac’s beck and call (Enright was a friendless doormat, but that’s a other rant…). Mac’s job was as an appointed person that sets policy for the police. I’m not even sure in real life if they handle budgets. And in real life, SF has more than one at a time,
I don’t know what it is in SF. In some places the police commissioner is a civilian but in others they are not and it’s been many years since I watched an episode of McMillan and Wife. If he had a gun and arrested people I’d say he was a cop. If his detective sidekick did that, then okay. We’ll put the show in the same vein as CSI.
Let me guess…Fred MacMurray’s character on MTS was actually his character from ‘Double Indemnity’, who managed to escape the cops, establish a new identity as his MTS character, marry, have the titular sons, then killed his wife (probably for insurance reasons again).
Not to mention Psych, which has more murders in a single season than Santa Barbara had during the show’s entire run (not to mention multiple serial killers)
Not quite; Walter Neff was definitely getting the electric chair as the end of Double Indemnity. But there was definitely something suspicious going on with My Three Sons with so many people disappearing that by then end of the run there was only one son left.
Stranger
Wow, I was too young to see the clues right in front of my face when I watched it as a kid, but now it’s painfully obvious that an orgy of familial serial killing took place on that show.
What about Petticoat Junction? The 3 pretty daughters kept changing, yet claiming the original daughter identity, and no one seemed to notice or claim otherwise. And there was definitely something fishy about Uncle Joe…
All with a kooky friend who gets into trouble
Yup, and a male significant other who doesn’t entirely approve of her amateur sleuthing.
(Why, yes, my wife is a Hallmark Channel addict. 
)
I can think of several that have a detective solving crimes.
Midsomer Murders
Dragnet
FBI
Hill Street Blues
Death in Paradise
Wow; great link! I’d never noticed that. Despite watching the show for its entire run and being roughly Chip’s age the whole time.
Then again, at the end Dad Steve is left with hot Katie, 20ish years his junior, and a new brood of little ones to kill at his leasure. Plus his second wife Barbara who was his age plus a bit. (taking the characters’ ages as those of the actors). In all, there was another 20 years of happy mayhem to go when the audiences and therefore the studios lost interest in Dad Douglas’ depraved and deadly depredations.
Done right (= very, very wrong), a reboot of this exploring the mass murder angle and the post-cancellation period could be a real hit with our geezer demographic. 
Would you prefer that all three (actually four) sons stay in the house into their mid30s as they did on “Bonanza” taking orders from their father?
Who you callin’ a geezer? 
Talking about Bonanza, what was the average lifespan of a Cartwright bride?
Stranger
More important, was there ever an official inquiry as to why they all had such short life expectancies?
Like, three episodes, I believe. 
Don’t get me started on the son who “disappeared.” Ever wonder why he up and decided to move everyone to California?
“Hoss” was apparently bigger than we knew. Wrecked 'em? He damn near killed 'em. Those poor girls!
Well, they would think that if they weren’t all just stories from her books. I mean, it’s in the title.
(Not a real spoiler.)