Poor Terry Matalas. It's clear from numerous post-season interviews that, for as elaborate as S3 became by the end (rebuilding the Enterprise-D! Bringing back Ro and Tuvok! Changelings and Borg and Lore!), his original vision was yet more elaborate. Apparently he originally planned to have Janeway and Kim also appear, and to show Ro still alive in the brig with Tuvok at the end of the season. The man clearly was dreaming big.
Given that, it seems slightly implausible that he would omit material purely out of carelessness. And the absence of Alexander seems like a pretty large omission -- especially in a season that was so focused on the parent-child relationship and the idea of "the next generation". Yes, there are all these memes about Worf forgetting Alexander, but that doesn't strike me as the kind of fan service Matalas was going for.
From a storytelling perspective, omitting Alexander seems pretty similar to why Odo was mentioned adoringly as "a man of honor" but not named: there was already a lot of backstory and reference being woven into the story, and throwing out a random name -- or a random concept like, "Oh yeah, Worf has an estranged son" -- would create too much to unpack.
Likewise, it seems like they wanted Worf to have a paternal presence with Raffi, so omitting Alexander simplified that story.
But still: in a season that was all about parents and their children, it seems significant that they couldn't find any way to reference him.
Unless...
Worf has a memorable scene with Raffi where he tells her, "Don't presume to know what I have sacrificed" (or something to that effect). Surprisingly, that line is never followed up on... explicitly.
But I suggest that that is where we learn of Alexander's fate: Worf has lost his son. Whether to death or desertion or deep undercover work, who can say? But we have an open question -- where is Alexander? -- and we have a vague statement that is never otherwise explained -- that Worf has sacrificed a great deal -- and given how much the rest of the season ties itself together, I suspect this was meant to be a subtle nod to explain away Alexander's absence.
Why not make it explicit? Why doesn't Worf tell anyone about Alexander? I argue it's because they wanted to save the "grieving parent" story for Riker + Troi, especially Riker. Explicitly portraying both Riker and Worf as grieving fathers would create an elephant in the room too big to ignore, and would've taken up much more space in the story.
So, instead, poor Alexander is consigned to a mysterious comment from his father -- perhaps fodder for some future tie-in novel, or perhaps someone we might meet in Star Trek: Legacy.
Are there other theories as to where Alexander might be, or why the writers did not mention him?
I wonder if Alexander eventually followed up on his desire to bring peace between the Houses and ended up dying instead of Worf? Maybe he somehow learned of Worf’s fate and decided to intervene, ultimately sacrificing himself to save his father. That might be part of why Worf has changed so much; embracing the things that Alexander believed in (peace and calmness) and making it a part of who he is in honor of his son.
I hate to think of Alexander as dead, but at least as a Klingon if he went out fighting for his father it was an honorable way to go.
This is my thinking too -- if we are supposed to infer anything from Worf's apparent omission beyond just "Alexander is somehow gone", my guess is that we are supposed to reach back to "Firstborn" and assume something like the "prophecy" did indeed pan out, but with Alexander taking the fall instead of Worf.
If memory serves, this is how Star Trek: Online took his story... and ah yes, it is indeed: https://memory-beta.fandom.com/wiki/Alexander_Rozhenko?so=search#Star_Trek:_Online