To be fair to the producers, for the last few decades now those kind of stories do seem to have had a much wider appeal that more positive optimisitic stories.
If they're done well, yeah, but
War of the Worlds season 2 was very badly written, and it just wallowed in the nastiness while having little point to it. Plus it was just so
literally dark all the time, the sky perpetually overcast when it wasn't night, that it was depressing to watch. In the episode where they went back in time to just after the events of the 1953 movie and we actually saw
daylight for the first time all season, it was so refreshing. (Although the past portions were inexplicably in black and white even though the movie was in color, and it made no sense to use black and white for a time travel sequence rather than a flashback or something. Also, if the present-day world was so grim and perpetually dark because of the long-term aftermath of the invasion, why was the sky clearer immediately after the invasion, when it should've been darkened by all the smoke and soot and dust from the worldwide devastation?)
The one time it worked was in the episode where the team strove to give the female lead's teenage daughter Debbie a happy birthday despite the grimness of the world they lived in, going to great lengths to extract some tenuous threads of positivity out of it all. That was one of the very few season 2 episodes I actually enjoyed.
OK, that does sound like fun. It could be fun to see the Star Trek characters would react to being in a full on epic fantasy world.
Back in the '90s, my best friend from college, who was a big D&D player, had the idea that we could do a 2-person RPG called
Dragon Trek over e-mail, where I would play a
Star Trek character sucked into a D&D world with her as the DM -- sort of a way to ease me into the RPG experience without throwing me off the deep end, and allowing two friends with only partial overlap in our interests to share a common experience. That was where I created the T'Ryssa Chen character I introduced in TNG:
Greater than the Sum years later, although in the game, she was named T'Lyssa Chen and she wasn't as quirky and neurotic as the novel character (though her backstory was the same aside from being a few years earlier in the timeline). It was fun for a while, but we didn't get very far before my friend's family commitments took precedence. But the incongruity of a Starfleet science officer finding herself in a high-fantasy world and trying to make rational sense of it was what we found interesting about the premise.
And of course it would be out-of-continuity; these big splashy different-genre IP crossovers always are. (Pelia may reference the Doctor, but she’ll never mention that time I just made up when she teamed up with Elric of Melnibone — though ironically, Moorcock’s multiverse could handle that just fine.)
It's easy to rationalize Pelia's reference to a time-traveling doctor as someone else, since there's plenty of time travel in the Trek universe, and plenty of doctors (medical or otherwise). We know from "A Matter of Time" that there are time-traveling historians in future centuries, and one can have a doctorate in history.
That isn't necessary. The Magicks of Megas-Tu was about an alternate universe where real magic existed, so there's already precedent for it in Star Trek.
Or rather, an alternate universe whose physical laws manifested in a way that resembled our concept of magic. Which worked for me because they were profoundly alien beings that only presented themselves as humanoid for our benefit, so it wasn't the kind of contradictory premise where the physics is different but Earth, humans, and specific individual people nonetheless exist.
I think they can be enjoyable. That's the key thing not to lose sight of: crossovers, mash-ups, whatever are supposed to be fun, first and foremost. And of course, there's always the easy option of "we're trapped in malfunctioning holodeck" or "Q did it" to explain away worlds that don't match up...
Which is how we got canonical "crossovers" with Sherlock Holmes and Robin Hood. And
Red Dwarf had Pride and Prejudice Land in its artificial reality simulator, which is sort of like Captain Janeway's holonovels.
Still, I generally don't like to cross the streams. I've sometimes dabbled with the question of whether I could cross over characters from different universes in my own original SF, like having Emerald Blair from
Only Superhuman meet the gang from my Hub stories, but it always runs up against the fact that my different universes have different physics, histories, and cosmologies, which is kind of the point, since I like exploring the different possibilities. I've thought of ways I could rationalize them being alternate timelines of the same universe, but I decided I didn't want to, since it would undermine the distinct qualities and intents of the different universes. I don't like the idea of effacing the differences that give things their unique character and identity. Those differences are a key part of what makes them worthwhile.