Maybe I'm not familiar with LotR enough, but I don't see what would interfere with it in DW... You even have Sauron and his mount Doom to cospay Death and her Black Citadel of Death.
The issue would largely be that DW characters are, regardless of how you use the moves etc., mechanical badasses. And the moves reflect that, including the default moves, which are highly focused on a take on D&D, particularly one leaning towards as sort of badassified take on pre-3E editions. The moves in DW are designed to funnel you towards a specific mode of play, which is a great deal more "power fantasy" than LotR is typically understood as - it's like everyone is Legolas and Gimli and Aragorn - and the movie versions at that.
D&D isn't great for LotR-type stuff either, and indeed a lot of fantasy RPGs aren't, which is why there are always LotR-specific or LotR-emulating RPGs kicking around, which tend to have a very different fundamental tone to them.
Are we ignoring generic systems like Hero and GURPS (leaving aside how much you like or how good you think the options there are for the moment)? Because they certainly have plenty of them, especially the latter.
We are somewhat unfairly not including them in the "actually designed" category, even though you, from direct experience, know HERO/Champions is. I mean, why don't I exclude HERO, because I'm only familiar with it in the context of emulating superhero stuff. However, I have a lot more experience with GURPS (albeit only up into the early '00s).
With GURPS, it feels like there are two things that differentiate it from "actually designed" systems:
1) The initial foundation of the game is from a very naive era of design, and some of the early design decisions in the game, appear to be naive, or perhaps the product of incompetent design which appears to be naive. The end result is the same and indistinguishable. So GURPS is supposedly generic, but some elements of it appear to be pretty specific (and naive) in much the way D&D is. Later editions didn't seem to want to change this (perhaps they have now, of course), which leads me to:
2) The "Prime Directive" of GURPS appears to be "Maintain compatibility and where applicable continuity with GURPS, even at the cost of being genre-appropriate".
This is evident for example with GURPS Fantasy. GURPS Fantasy was a mess (using past tense, because maybe they fixed it). It did not provide tools to emulate the fantasy genre at all, nor the various subgenres within fantasy. It talked a great game - describing a lot of that stuff and doing so well ("talking a good game" is basically why I have so many GURPS books, because they tend to be useful well beyond the rules, which are often lacklustre). But the rules it offered don't actually support the genres it discussed. For example, it had an extremely specific approach to magic - just as specific as D&D - despite a lot of "talking a good game" around it - and then it had a lot more on magic, but which all pretty much builds on that incredibly specific take on magic. And the reason it took that approach wasn't that it was a well-reasoned take on magic which fits with the fantasy genre, because it didn't (and I see no period in history when that would have been the case). It's because it's the approach GURPS Fantasy has always taken.
And if you look at the genres, there's no mechanical support for most of them beyond attempting to model various monsters etc. in GURPS terms. Like, nothing is going to push you towards classic tropes of specific subtypes of fantasy, and the game will still always play out like GURPS - replete pretty highly deadly combat, over in seconds, which is quite skill-reliant. Occasionally you see an optional rule to simulate one small element of a genre, but even that is extremely rare, even within genre-specific books.
Let's not even start on GURPS Supers. It certainly shows that, comparatively, HERO was extremely committed to genre emulation.
TLDR: GURPS talks great about genres and themes and so on, and provides a ton of material in a literary sense, but when it comes to mechanics, tradition/continuity (i.e. how earlier GURPS versions approached something, no matter how naive they were) and interoperability between GURPS material will always trump other factors.
EDIT - Particularly relevant to this thread, AFAIK GURPS has absolutely no way to approach heist as a genre that D&D doesn't. It arguably has better rules for them on a basic level (3d6 resolution, narrower range of TNs, etc.), but you'd have to run it as plan-execute, and you'd have to pretty elaborately model the heist building and guards and so on, which would be a kind of anti-support almost (worse than D&D because more work would need to go into it). This is indicative of the general attitude to genre in GURPS. Provide rules on top of the GURPS rules, but which don't fundamentally change assumptions or alter approaches. Generally GURPS leans extremely hard into simulationism (and away from gamist or narrativist approaches), and not of genres, but of this sort of unspoken "the way the world works", which is basically GURPS-world. If characters in a setting are all tough, GURPS will say "make everyone buy 10 levels of the Tough Guy advantage" (fictional example), rather than changing the damage rules, which will still be basically murderous.
SECOND EDIT - Total aside, but do you have any insight into why Champions went for this pretty complex/fiddly "squad combat" motif in its combat design (particularly stuff like segments)? I'm guessing it was before your time and my presumption would be that it came out of familiarity with various wargame-ish concepts, and as such I would characterise that as "naive" design, but perhaps the actual thing was that they wanted a highly tactical superhero game, not one that emulated the genre and its tropes and so on.
