The real world analogies of Warhammer are not preciselly a hidden secret, no one is putting that into question, but I hope that you'll agree with me that when I say "New York" (to make an obvious example), 99% of people will instantly get a very specific image in their minds that is quite hard to bypass no matter how invested in the setting they are. If knowing how the extremelly iconical New York looks is a "fault", then I guess that's the "reader's" fault.
Now get that very iconical place and make an scale ranging from New York to Genericnameburg. The stuff closer to New York is the stuff one should avoid to achieve immersion. Some other stuff in the middle, like the Great Wall of Ch...Cathay, hurts no one. It's a "medieval" (to simplify) Fantasy setting, I can see Great Walls fitting there perfectly, but skyscrapers just don't. As for clearly referencing real world places, like Cathay, as far as I'm concerned, Warhammer is not trying to (and IMO shouldn't) tell you "hey, you are in China, but there are orks here", it's more like "you are in this place with a very oriental vibe that sure as hell looks a lot like China but it's not". That slight difference here can be huge to a) distinguish itself as its own fantasy setting and not just a lazy analogy and b) desvinculate the player from the real world and immerse him in this new, different setting (which is the whole point of fantasy, after all).
To do that, having places like "Běijīng" probably wouldn't help, having places like Tōngyòng zhèn (according to Google Translator, "generic town") is much less disruptive (and please don't take that literally because it's not meant to). (Also, Beijing is much more easily associated with a medieval setting than New York, but you get the point)
A point to be considered here is that not all "works of literature" should be respected the same for the only reason of being a "work of literature". As subjetive as "art" is, I think it is however quite feasible to say that there is good, mediocre and bad literature. Your take (correct me if I'm wrong) is that Warhammer is just "different", with it's own aims, and therefore shouldn't be judged, and my take is that, different as it is, Warhammer is not good literature and therefore can be improved, and improving it should not necesarily be detrimental for its uniqueness.
A Song of Ice and Fire (Game of Thrones) also takes a lot of obvious influences from real world places and events, such as The War of the Roses in medieval England or islamic Spain (hell, Westeros is a carbon copy of Ireland), but still it feels like its own thing, like a different universe, and I doubt that that would still be the case if Westeros was named Ireland instead. Now that you mention an analogy to the Mongols... do you think it would have been better for achieving immersion to straightly name the Dothraki "Mongols" or "Huns" since they are an "obvious analogy" of them?
The references are obvious in both cases (every single fantasy or sci-fi creature, nation or land is a direct reference to some real world counterpart, humans are unable to imagine things they have seen before. "But I've never seen a gryphon in my life!", yes but you have seen an eagle and a lion, haven't you?, "And what about aliens?, no one has ever seen aliens" well, most of them are actually reimaginations of fetuses, insects or some other animal, so no). The references are always going to be there, the art is to hide them, to make them subtle. One could argue that someone might want to create some kind of "alternative history" or "paralel universe" which was almost identical to, say, medieval Europe, but with dragons and magic in it and having Joan of Arc ride into battle riding a warg instead of a horse, and it would be legit from a design point of view, but that's not the case with Warhammer, since I think it's quite clear that they have at least tryied to "deform" it enough to make it different. The mistake is, in my opinion, falling in middle ground. You need to have a clear artistic direction when creating something. Do you want a real world analogy or do you want a proper, fully fledged fantasy universe? I really dig the whole idea of Warhammer having obvious analogies to real world stuff, but I think that their aim was indeed to use those analogies as references to create a proper, differentiated setting, and my humble opinion is that the setting is not executed well enough (after all it was an afterthought, Warhammer has always been first and foremost about playing tabletop batles with miniatures, not about writting serious novels).
Summarizing, I doubt that any writter that wants to create a medieval fantasy setting names the capital of his empire "Berlin, heart of the third Reich" if he has any intention of making the reader immersed in it and then blame the reader if he fails to do that. In Game of Thrones, you actually have to make an effort to picture Ireland, but if in a fantasy fetting you get "the hordes of chaos have just attacked London"... well the recurrent image is much more immediate and harder to avoid.