This isn't targeted at any specific game, though I'm likely to criticize both 3.x/PF1e and 5e because they are (in some sense) the "old guard" and "new hotness" on this topic.
So, there are a lot of motives when designing a game, and I do not mean to comment on the spectrum of reasons one might consider. That's well above my pay grade. However, something that I don't think is so far above my pay grade is arguments in favor of rules elements, structures, or principles because they make the rules look/feel nice, without regard for the potential costs this can have to designers, DMs, and players. I'm not talking about a desire for good art/presentation, nor for flavorful descriptions or concepts supported by the rules. Rather, I'm referring to a desire for rules because they have satisfying aesthetic features like symmetry, one-stop-shopping reference lists, brevity, and (possibly the most controversial on this list) natural language. The former things are just regular aesthetics, whether aesthetics of the physical materials or aesthetics of the play experience. I'm talking about "meta-aesthetics," for lack of a better term: aesthetic concerns purely at the design level, in some sense "before" the aesthetics of the materials or play-experience.
I see a lot of arguments that, in effect, treat these meta-aesthetics as one of the most important features of game design. Many people trying to "fix" 4e, for example, are incredibly keen on condensing all powers down to either a per-source list, or to even a single list for all classes. The reasons given rarely have much of anything to do with direct design concerns like effectiveness or testable mechanics, and almost always ignore stuff like "what about powers with subclass-based riders?", instead focused almost entirely on the bald assertion that a single, repeatedly-referenced list is always superior.
I don't think I'll surprise anyone by saying that I disagree with this, and with most other meta-aesthetic arguments about the ways we structure our rulesets. Meta-aesthetics are NOT an invalid reason to design something. They can, in fact, be great! My arguments for why it was good that power sources existed in 4e (re: it gave us some really cool classes like Avenger and Shaman) are, at least in part, based on meta-aesthetics. What I find frankly a little disturbing is the axiomatic insistence that (some) meta-aesthetics override effectively all other concerns. This belief, asserted without defense and indeed with an implication that it needs no defense, that sacrifices of balance, at-table experience, design space, and indeed pretty much any other element of game design, are almost always worthwhile if they produce rules that have "better" meta-aesthetics. That it takes a LOT of serious problems for even a small meta-aesthetic gain to be put off the table.
Now, it's entirely possible I'm just not hearing what's actually being said--it wouldn't be the first time. I am, as always, open to having the record set straight. I'm also open to people defending why these meta-aesthetic concerns should have more weight than I've given them up to now. But either way, I think we can benefit from dragging this implicit assumption out into the open and having a talk about what weight "rules that look nice on paper" etc. should be given.
I don't think you are WRONG by any means, but I DO think there are definite benefits to certain kinds of 'elegance'. For one thing, I believe there is a 'complexity budget' that games are going to need to meet. Now, D&D MAY BE DIFFERENT! As the original and archetypal RPG its weird quirky rules systems and vast quantities of material and background are kind of part and parcel of the game. If anyone is going to play TT RPG they are vastly likely to simply land with D&D and it will be THE option. Relatively few people go on to any other game, and even if you don't master D&D, you can play along with the geeks in your group (and there surely will be some in most groups).
HOWEVER, for other games, such as if I am a game designer making an RPG, this is NOT true. Players are limited, they have limited amounts of time and energy to master rules, and generally demand high "bang for the buck" in such rules. Now, I think 'content is king', so it is likely that the effect of 'good rules' is uneven, as a game with really elegant rules, crummy presentation, and an uninteresting or badly presented content (IE setting, premise, etc.) will undoubtedly fail with most people. OTOH, all other things being relatively equal, a great set of rules, cleverly deployed, can provide a game with a distinct edge. Of course the two need to support each other as well, if your rules don't synergize with the premise and advance the desired game play experience, then things won't work.
All of that being given there are a few things that good, simple, elegant rules systems can do for you. The first is that they can provide a UNIVERSAL LANGUAGE. That is, in a game system like old school classic D&D, like say AD&D 1e, there is a big problem. Every single thing that may come up in the game is represented by some completely different subsystem, which uses different kinds of dice, etc. Nothing can be compared to or integrated with, anything else. There needs to be a rule for every specific thing, like "what happens to my initiative if I'm injured?", or even "what is the benefit to initiative of a high DEX?". This quickly increases complexity and creates both a burden on the GM and uncertainty in the mind of the player as to how the fictional world actually maps onto the resolution system (and thus uncertainty about what their abilities mean).
D20 was a huge advance in the sense that it unified all of these things. Now I simply know that everything dealing with how quickly and accurately I can move and act is a check modified by DEX, and it is all done on a d20 against a target value, and there are a pretty small number of standardized target values (in 3e it was AC, or a conventional set of difficulties, 4e got even more precise about this, and 5e is equally precise most of the time). If some completely novel situation comes up, the GM and player already have agreement on how it is handled, and the player can evaluate his options with some confidence that the GM won't suddenly require an unmodified d8 roll needing an 8 for success, or something like that.
Likewise the benefit in complexity budget should be clear. If a player need only learn one core system, then they are ready to play almost right off the bat. Their investment in mastering rules is much reduced, and you're vastly more likely to get people into the game than if it takes 100 hours just to fully understand how combat works. There are going to be a few people who find such simplicity offputting, but in this day and age when people have vast amounts of calls on their time, it is almost surely a winner.
Another advantage is in terms of presentation. While the details of presentation are closely related to the 'content' side of the equation, they are certainly made more tractable if you don't have to present a vast number of different elements simply to cover all the rules system bases (or else simply leave most of it to the GM to slog through). This is the nature of the vaunted GM friendliness of 4e. It is a real thing too, even its fairly simple stat blocks give you a monster that can interact with every rule in the system, as needed.
And this parsimony lets you put the real complexity where it can do its best work. You can elaborate a subsystem, or build 'side systems' that are mainly useful in building up the milieu or presentation. So, a really good example is Traveler, where the core system is extremely simple. There are a wide array of 'side systems' which build on that core without cluttering it up. The GM has entire systems for patrons, starship operations, law, culture, society, planetary conditions, wildlife, etc. etc. etc. None of these impacts the basic skill resolution system at all. The only one the players normally even see is the character generation system, which normally happens offline and is itself pretty straightforward (though it is perhaps one of the more complicated and often elaborated subsystems of the game).
Traveler, in contrast to D&D, has survived virtually unchanged since the 1970s. Material produced for the earliest editions of the game meshes perfectly well today with 'Mongoose Traveler' and also with 'T5' (Marc's own most recent version). There were a couple of aborted diversions into variant rules systems, but none of them could really compete with the raw simplicity and elegance of the original.
BRP (the core system of CoC as well as Runequest and a few other games) can be cited as another example. It is an extremely simple system which has remained pretty much unchanged in its core mechanical structure since it first appeared in the 1970s, although a number of quite different games have been built on that base.
My advice to game designers today would be to make every attempt to emulate these games of the past, and eschew the complexity and lack of orthogonal rule structures which tends to exist in D&D. D&D is successful and I'm not arguing we should change it, just that it is kind of a special case. You will almost never be in a position, designing a game, where that game is even likely to be played as much as D&D by the people using it! At best its greatest supporters and advocates might do so, but their players probably took a break from a 5e campaign to play, and aren't likely to have the time and energy to absorb 12 different heterogeneous subsystems. You are doing yourself a service by sticking closely to one or two constructs and building around them.