2- mythology
There are other reasons why elves are hard to describe, noticeably because of their DnD mythology.
First I would like to point out that DnD elves are not Tolkien's elves.
The DnD game universe is really like a sponge absorbing pieces of lore from so many sources. Even though it is obvious to me that Tolkien's popularity had a huge impact on the DnD content, the DnD elven lore has many references to how elves were perceived, in our real world, across the centuries.
In the cosmogony and in the mythology, DnD elves are modeled on that of real world lore and legends in a quite chronological manner.

At first they are chaotic, shapeshifting, free-flowing like their chaotic and invisible european model.
When some of them decide to become more "defined" and then adopt an elven identity, thus renouncing part of their fundamental chaotic nature, a conflict occurs. Their greater god casts them out of their homeland and a diaspora takes place.
No doubt you'll find all the details you want on the Internet.
All of that is a DnD myth but it helps to better comprehend and substantiate the elven nature.

The part I'm interested in is their new main homeland: the feywild of self-descriptive nature.
Again it's akin to the mid/late middle age elves seen as fey, and as such, creatures in realms of enchantements and illusion (at least in continental Europe + British Isles)
There the elves take shape, modeled after the Leshay. Not a helpful reference because this is a chicken and egg problem, the leshay being described as albino elves. However this indicates that the prime material creatures, including humans, are not their functional model.
In a world so imbued with magics, it is easy to understand how difficult it would be to proceed to the definition of their canonical appearance. By the way the so called nobles, or the most elv-ish of them so to speak, named Eladrin, are still able to change their appearance to some extent.
The environment is also effective at generating sub-races. AFAIK the sun / moon / green / dark elf subdivison predates their arrival on Toril.

Our artistic representation of fairies is quite unrestrictive, obeying no standard. Anthropocentrism remains the main constant though. And of course there is the witch trait archtype when there is a need to describe the creatures as scary or spooky. Same thing with DnD elves, it is very contextual.
Among the works that influenced DnD, there is one particular source describing slender, high cheek bones, pointy ear creatures, these are the dark elves in Anderson's literature (let's be honest I haven't verified). Yes they just need to be scary whereas the light elves, their counterpart in (part of) the norse mythology, are reputed for their beauty.

Incidentally, as DnD elves are not Tolkien copy-paste, themselves influenced by their norse ancesters, they have no reason to inherit the fair-folk cliché / euro-morphotype associated (for debatable reasons) to Tolkien's elves. Well on condition that you do not mistake one for the other.
Similarities between the two narratives do not help though.
Moreover elves spread over all the continents when they came to Toril. If they had to adopt yet another precise morphotype there is absolutely no reason to specifically take the faerunian, supposedly caucasian, model. Ah and btw humans were not yet civilised enough to interact with elves.