I believe Rizzoli & Isles had 13-episode seasons, which is probably easier to manage than the standard 22-episode broadcast network season. Just guessing…
The actress wanted to take a part in another show. So they killed off the character, rather than having her quit.
The death of Matthew was particularly weak. After they’d gone to the trouble of having him dramatically stand up out of his wheelchair in a burst of spontaneous healing earlier that season.
Sybil’s death was OK, as it allowed the opportunity to work the Spanish Flu epidemic into the story line. Not to mention driving a wedge between Cora and Sir Robert - she accused him of being slow to bring in the trusted family doctor, because Robert was afraid of offending his titled associate (also a doctor), who said Sybil would be fine. Cora was right about that.
He lives on in the novels. His death was a ruse. Malcolm’s former commander in Section 31 recruited him to infiltrate and report back on the Romulans.
Because IRL nobody kills you out of spite because you want out of your contract. Um, except among your patients. 
They can go live on a farm upstate! I double dead dog dare a writer to go that route.
Not much a 1920’s doctor can do vs the Spanish Flu, no matter how good he is.
Hmm, interesting! And yet I don’t think he’d blend in too well in Romulan society…
Sybil didn’t die of the flu, she died of eclampsia after birthing baby Sibbie. The trusted family doctor was there and flat told them what it was, the “best” obstetrician in England that Robert brought in under the aegis of giving his daughter the best possible care was the one who handwaved it off.
Lavinia, Matthew’s fiancee, was the one who conveniently died of flu in order to leave the way clear for him to marry Lady Mary.
I like dogs as much as the next person, but anyone in that situation who runs back to save their dog and loses their own life is a bloody idiot.
You’re right, I got some of the stories mixed up in my head.
Getting old… sigh…
I don’t know why Maude Flanders had to die.
If you think that, you weren’t paying attention.
The death of the Meg Ryan character in City of Angels (a literal truck ending) came out of nowhere just to lay the irony on with a trowel.
Nope, still pointless. Yes, they tried to make it not pointless, but a alive Mrs. Landingham could have given the same sage advice, rather than a hallucination, which makes us doubt if the President is sane.