“We’ve always had an Ensign Kim. We must always have an Ensign Kim. The sacred logs of The Janeway speak only of Ensign Kim, and so it must always be.”
The most logical time to kill off Wesley Crusher would be in “Justice”, s1e8, when Wesley was condemned to death under a planet’s local laws. In the name of respecting the local culture and maintaining peaceful ties with the Federation, Picard allows them to execute Wesley. For the next three seasons Dr. Crusher is bitterly resentful, all but mutinously hostile to Picard, and only very slowly and grudgingly lets go of her grief and wrath.
And no, I can’t spend the next two hours researching how Wesley was pivotal to later episodes and explaining away how they did without him. I’ll just presume something worked out.
I don’t think Beverly would be mutionously hostile to Picard. That’s not her style. But she’d definitely have insisted on an immediate transfer at a bare minimum, and more likely have resigned her commission entirely.
“The cloning farms on the Hollow Deck, we built them to insure that we keep this sacred charge!”
(queue shot of multiple tubes full of Harry Kim clones)
Season 7, episode “Genesis”: the de-evolved Worf spews venom into Brannon Braga’s face. Recoiling in pain, Braga slips on a slime trail left by a de-evolved Troi, and falls into the web of the Barclay-spider, which devours him, thus ensuring that he will never write another episode this stupid.