I think part of the problem is that there are actually different authorial voices in Tolkien's work, especially (because it's all in one work) in LotR. There's the light, even comic style of the earlier chapters (with some dark patches, such "The Return of the Shadow" or "The Old Forest"), there's the blending of old and new in the chapters in Breek, the journey to Weathertop and then to the Fords of Bruinen; a contrast between the almost pedestrian, nineteenth travelogue style used for description from the hobbits' point of view contrasted with glimmerings of the "high style" in Rivendell; the growing use of that "high" or antique style as we get further into the older kingdoms, the history of the realms and the war and its causes, etc.; and then a shift back toward a more colloquial style as we go back toward Hobbiton. All of this embedded in a very dry, professorial tone dealing with the histories, languages, etc. (which really are an important part of this book and shouldn't be left aside unless you're just in it for the story proper; if you're wanting to know what the writer was doing, read the preface and the appendices; they put the book in the perspective of history, which is what Tolkien intended). This is why I think Tolkien was actually a very good writer -- he used a wide variety of "voices", but all modulated through the eyes of his main characters, the hobbits; and even there one can see shifts, as if part is written by Bilbo but altered or updated slightly by Frodo, and then others as written by Frodo but having gone through various redactions, and finished by Sam -- and all brought down by writers who copied and in the process made slight, subtle changes as with any such history; and finally rendered from the languages of the time into modern English by Tolkien himself; so we have a vast number of removes: Tolkien>old historians>older (official) mss>Peregrin (as Thain)>Sam>Frodo>Bilbo, and probably a few steps I left out. Now, that takes enormous skill and a great deal of effort and thought and careful choice of words and phrases (hence, since Tolkien is "translating" for modern audiences, we have the bizarre image of an express train in "A Long-Expected Party"). One is free to like or dislike (I personally used to find the earlier parts of the book rather annoying, until I began to realize how the voices changed to suit the "originals", etc., and then began to be really surprised at how well it was done), but if one looks at what he was attempting, it's difficult to deny that he did an exceptionally fine job with an almost impossible task. Most writers today esches this sort of "chinese-box" structure and simply use either a first-person narrator or omniscient pov; this sort of thing takes immensely more effort and is slippery as the very devil! (Remember, too, that Tolkien's profession was dealing with philology, the study of literary texts -- especially ancient -- and establishing their traditions and transmission, by use of historical and comparative linguistics; Tolkien was extremely sensitive to nuances in prose rhythm and style and what they tell of the culture and person(s) who created them; and he brought that to bear when writing his story. This is something he shared with Lovecraft who, though coming to such a study on his own rather than academically, was very aware of such things, and tended to choose his words carefully for very subtle coloring and to convey nuances in the narrator's -- or occasionally, in his third-person or omniscient narratives, his main characters' -- emotions and psychology. It's a much older and more carefully structured way of writing, and completely at odds with most of twentieth-century literature's immediacy of effect; but it allows for more depth and texture and considerably more interpretability.)
The same is true, to a lesser degree, with some of his other writings. The Silmarillion, of course, he never completed nor polished; the book of that name was put together by his son Christopher from writings spanning 1914-15 to just before Tolkien's death in the 1970s; and so the style is by no means as homogenous as Tolkien would have liked; even so, it tends to be more of the "high style" than LotR (and certainly more so than The Hobbit, which was written with a much different view in mind); but even within it, there are various literary and "historical" "traditions" within the "transmission" of the work(s).
In one sense, Tolkien did finish the sort of thing he did -- he didn't actually start it, it had been done by older writers from the 1740s on, if not before -- but it's unlikely we'll ever see anyone else put that kind of thought into that large a variety of factors before putting pen to paper (or fingers to keyboard, as the case may be).
In other words, Tolkien simply wasn't modern at all; he was, perhaps, the last remnant of a much older tradition (as Hawthorne was of his); and that difference may be what throws people off at times.
