That's kind of the problem - if you did do an Eberron movie first, then that becomes the baseline. If Marvel had made GotG first, rather than Iron Man, it might still have been successful, but the MCU followed would have looked very different. Much more space based and less room for darker more serious material.
And, IMO an Eberron movie would be just that - an Eberron movie. Not a D&D movie. It might be a great fantasy movie but it wouldn't be any more D&D than Conan or Krull or Dark Crystal or Frozen.
But how is that "the problem"? Or even "a problem"?
If you do an Eberron movie, Eberron is still generic enough that it fits within the large box the general public (certainly under 40 or 50) considers fantasy, alongside things like LotR, The Princess Bride, Labyrinth, Final Fantasy, Stardust, Conan, and so on. It's not so outre that it seems like something else. It's not going to make people surprised if a different D&D movie doesn't have trains or airships in it (though, tbh, an FR movie easily could have airships, because the FR has had airships.
Or Sharn, City of Towers. People don't expect every city to be Sharn, just because Sharn is.
Or how people dress in Sharn - again, it's within the bounds of "fantasy", and so is how people dress in the FR (indeed there's probably a 1:1 crossover in a lot of places).
Eberron is an extremely broad setting, and I don't see anything about it, that's not equally likely to cause problems if you're starting with FR or with Greyhawk or wherever. All them contain minor incompatibilities, like the elves aren't wholly compatible, but aesthetically Eberron is just essentially a more exciting and less "Your Dad's Idea Of Fantasy" take on the same
kitchen sink.
Now lemme make one major point of agreement -
this doesn't apply to all D&D settings. Some are too far outside that, such that if you started with them, there would be a problem. Dark Sun immediately comes to mind. Or Spelljammer. Most of the MtG-based settings likewise. Planescape is a special case but I think is probably best reserved "for later".
I think there's also a real difference between what you might call "misty" fantasy, like LotR, where atmosphere is very key, and "wild" fantasy, which is more of the Marvel/Indiana Jones kind, where it's more about style and action. I think there's a fondness for "misty" fantasy (is there a better or more formal name for this?) among people my age and older, but I don't think it's like, very "D&D". I think very few D&D campaigns play out like LotR, and loads, and loads, and loads play out like GotG or the like. So whilst I think a lot of people would like this sort of sedate, sensible fantasy movie, maybe set in The Dales in the FR or something, or maybe a particularly calm version of Waterdeep, I don't think that would be any more D&D, than, y'know Frozen is. It would be a "Forgotten Realms" movie. Whereas Eberron, like it or loathe it, is better aligned, intrinsically, with how most D&D, to judge from all accounts I have available - not just my own experiences - the accounts of people here, let's plays, podcasts, long-running shows like Critical Role and Acquisitions Incorporated, and so on. Yeah some people are playing those calm, meditative almost LotR-esque games, which I honestly would love to play, but I don't think that's representative of D&D. D&D is dodging traps, whilst shouting friendly abuse at the idiot who triggered them and running headlong into a pack of enemies. It's much closer to the spirit of stuff like GotG and Indiana Jones than LotR. And Eberron works well with that. You can absolutely do it in other settings, but Eberron is peculiarly well-aligned.
I've said all this though and I think it's like a 95% chance it'll be set in the FR.