And D&D just happens to use arms and armour - things that are not consumer goods in the world most of its players are familiar with, and that most of those players wouldn't know how to extrapolate from for other stuff that is more familiar - as its benchmark?
Sometimes this can be an abstract - wealth ratings and DC checks or rank and quartermaster checks - but if this is something the game wishes to have in play it helps to provide benchmarks.
None of this addresses my point: if the argument against including the mechanical significance of fancy clothing is that each GM should individualise it for his/her table, why is combat gear different?
Which is exactly what I've been saying - there is no uniform resolution system, as combat has a fixity and a mechanical granularity that non-combat does not.
And in that way is also supported as a focus of play that contrast quite markedly with other fields of endeavour.
I mean pre-MegaTraveller. (I use the 1977 edition with a few mods drawn from the 1981 (?) updates, the Special Duty line on the MegaTraveller lifepath tables, and Andy Slack's Backdrop of Stars articles in White Dwarf.)
Classic Traveller has price lists, but those aren't what tell you what the gameplay purpose of money is. That is ascertained from the rules for combat, for bribery, for interstellar travel, and for world exploration.
DnD designers *chooses* to provide arms, armor, mounts, day-to-day services and expenses, vehicles, carts, food, booze, parchment, inks, perfumes, fine clothes etc etc etc to give a fairly broad comparision of things as benchmarks - some of which are realtable to the IRL of its players and others which are not relatable IRL and that allows the players a form of cross-tab basis.
As for the need or desirability of a fancy clothes mechanical system to be added or included...
The fact that different weapons and different armor provides distinct drfined mechanical differences is typically a desired granularity level for a game with a fairly technical combat system is not surprising or unexpected. Its fairly status quo. It would be jarring or a disconnect to have one without the other.
But this will vary from the game type. A game with much less expectstion of combat scenes or seeing less tactical resolution might have very little - even turning weapon type into just a cinematic flourish. Chargen would also tend to focus less on combat type stuff.
For many swords and sorcery type games/settings in TTRPGs the idea of applying that same level of gear related granularity to every facet of play doesnt usually ring "true" to the genre.
How many fantasy movies or novels do you recall where the choice of non-magical clothing played as much to the plot or advancement or resolution as the hero arms and armor did? LotR many of their weapons had names - some fans can tell you them, the mithril shirt gets its moment of spotlight... But what was the name of gandalf's sandals? Should we represent that source material with rules for how much gandalf needs to spend on those sandals to help with his intimidate check?
Most of the players i have encountered would not be as expecting, accepting or even immersively inclined to see tables of "blue silk shirt +1 intimidate" type gear expansive detail as they see in arms and armor because it is a departure from,the focus and direction the spurce material takes the game is trying to represent.
They would be sooner willing to accept or expect better deep dive gear details of say foods (impact on healing or resistance or carry), alchemy and medicinal herbs as various media and source tend to spotlight those.
If one was playing a setting for a culture where high end social ettiquette is key (thinking japanese old samurai stereotypes) then one would expect to see more details for "type of garments gsins you this" and "tea set made by so-n-so gains you that".
To me, just as an observation, the idea that a game system needs or benefits from a universal resolution mechanic is a trope trotted out now and again that is mostly not true in,my experience.
Games are not served by having the same redolution in the same detail for cooking the evening meals, performing an artistic dance, trick riding on a combat field, winning a poker game, fighting a duel, etc etc because i just have not seen a setting or game where for the typical play each of those served equal import to the play and story.
When its tried, its more of a non-resolution indie thing where its more authorship than resolution and its more about screen time than "how to use..." be it gold, weapon, blue silk shirts etc.
Ymmv.