Would it though? Star Trek's Klingons were originally inspired by the Mongolians I think, but since that inspiration has no influence on the story, Trek has been changing the Klingons here and there and trying different things with them. From what I remember Roddenberry based a bunch of the Trek races on various Earth cultures, but... that's just inspiration. There is no in-story link between these alien species and the Earth cultures they were initially based on, so the Trek universe has been changing there here and there, since the initial inspiration doesn't really matter.
Keep in mind that Roddenberry's first glimmers of ideas for Star Trek happened the year after the Cuban Missile Crisis. His pre-Hollywood producer/writer career was as a cop, and there's a story that he went up to a producer once, while in his uniform, handed him a script, and asked him to read it. I don't recall the rest of this story, but the fact is that what was considered normal then is not what is considered normal or even very familiar now, in many ways.
1964, when Star Trek was born (it went through a considerable time in development, pre-production, doing the first pilot with Jeffrey Hunter, and having to do another one because the studio suits didn't understand it - apparently "human slavery/imprisonment is bad" was too hard a concept for them to wrap their closed minds around"), was during the Cold War. That meant many of the writers and directors, as well as Roddenberry and the other producers (ie. Herb Solow, Robert Justman, et. al) saw life in terms of WWII and the Korean War, and quite a number of them had seen military or police service of some kind. That was true of science fiction authors in general, as Heinlein served in the navy, and even Asimov got drafted.
So this generation of writers and producers wrote what they knew and what they thought would be familiar to their intended audience. Star Trek was meant to be a science fiction version of a morality play, with things Roddenberry wanted to show or get his ideas known, but wouldn't be able to in a more direct way. So if you call the "other side" aliens and give them alien makeup and costumes, you can still tell the same stories that might otherwise be censored or ignored or not understood.
The Klingons of TOS and TAS represented Communist Asia (Russia & China), and were made up to look Mongolian. This was the way they were depicted up until the Motion Picture in 1979 remade the Klingons to be more alien-looking, and from that point through the next four TV series (TNG, DS9, Voyager, and Enterprise) they were depicted as still representing an Asian society, but the emphasis had morphed into a warrior race more akin to the samurai, with the nuances of honor, weapons-culture (bat'leths vs. katanas), and TNG even introduced the concept of the "Klingon tea ceremony" in the 2nd season.
The Romulans in TOS were initially based on the Romans. Novelist Diane Duane's take on the TOS Romulans is better and more nuanced than they became after TNG introduced their version - all of them wearing the same bowl haircut, bumpy foreheads, and insanely shoulder-padded uniforms reminiscent of Sue Ellen Ewing's costumes in Dallas. The TNG version is bizarre since they're cultural offshoots of Vulcans who refused to accept the philosophy of Surak and left Vulcan to pursue their own interests a mere few thousand years before TNG and that's not enough time for evolution to significantly change their cranial anatomy. In the '80s, the Klingons morphed into an "honorable warrior" race and the Romulans became the new authoritarian one-size-fits-all "Evil Empire." Then the Cardassians were introduced, then the Borg, and so on. Every new Star Trek series that comes along introduces its own version of the Evil Empire that at least reflects and is meant to represent what they perceive is the "enemy" in mainstream American life.
So Star Trek can be flexible, up to a point. I gave up DiscoTrek because for me, they went too far, in too bizarre a way, in reimagining the Klingons. That, and a godawful boring cast of characters and an "f-you" attitude toward continuity with TOS, is what made me give up on all prequel series. I have ZERO faith in any of them that insist they're compatible with what they're supposed to become to remain in continuity with TOS. Even Enterprise was more of a TNG prequel than a TOS prequel since it ignored so much of TOS canon. I then tried out the opposite new type of Trek series - Picard - and when Icheb was killed off in such a brutal, gory way, that was it. I very much doubt I will ever watch any new Star Trek again. They (whichever producer/showrunner/whatever) blew their last chance with me.
Fortunately I've got decades' worth of stuff to read, whether it's fanfic or pro novels not read yet. And that's just the physical stuff in my library. I don't know how many Star Trek stories have ever been written, but I think it's safe to number them in the millions at this point. The ones published in print 'zines and the more well-known fanfic sites are just the tip of the lot.
Why would the initial inspiration matter in the case of Middle Earth? I'm honestly curious because I don't see why it matters.
The initial inspiration for anything will usually influence a great deal of how it develops. The more coherently it sticks together (like a cake or a pie rather than a half-cake/half-pie), the more the readers/viewers should be able to get into it, like it, and pay for more of it.
If you get rid of the Chinese-themed swords, IMO it doesn't matter who you cast as the Fremen. And I mean, it does matter, because the Dune universe is our universe, except in the far future. The Fremen are supposed to be descendent from "Zensunni travellers", and the implication is that these wanderers have Buddhist and Islamic roots of some sort. I could be reading into the story too much, but I always imagined them to be of a varied ethnic mixture of people. I feel that DV did it right by casting the Fremen with actors of various ethnicities. No East Asians there from what I saw, but I don't necessarily see anything wrong about having east Asian looking Fremen. In fact, I would expect some of them to look like that.
I guess Villeneuve couldn't wrap his mind around the idea that Chani's father had to be male, but I will concede that he was spot-on with casting Dr. Yueh. This actor fits the description in the novel, which is that Yueh looks East Asian. Of course I'm going by looks, since I haven't seen the movie and don't know how well the actor actually plays the part. I thought Dean Stockwell did a decent job in the Lynch movie, but he was just a bit 'off' when it came to meshing his portrayal with how Yueh was in the novel.
In the end Midlde Earth is a made up reality that isn't tied to ours at all, so unless the race is described to matter in some way that matters to the plot, I don't see why it would. That's just my own personal opinion though.
Okay, here's an honest question. Why is the LOTR setting called "Middle Earth"? Is it like the Pellucidar books by Edgar Rice Burroughs, and there's an actual other world in the middle of the one we know?