Regarding your tags on the class/race post, my first thought is elves have an ethereal beauty that non Fae minds can instinctually pick up on, which is diluted down to safe levels in half elves. Mechanically? The lever was thrown hard in the "make them distinct" direction
Before I address your actual ask:
THANK YOU FOR THE A-
(Sees spider profile pic.)
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Okay, I’m done now.
So, your ask.
The first can work as a justification. The mechanics, I think, are what you say (because the Int bonus is for High Elves only) plus a third reason:
Elves have been Magic Users since the original 1974 D&D box (when they advanced as “Fighting Men” and “Magic-Users” at once; they stayed Fighter-Magic Users through Basic D&D and have held the reputation for that ever since, but mainly in odd spots in the rule sets).
With AD&D, race and class split, but there were restrictions on which classes a given race could take, in which combinations, and to how many levels. (Humans didn’t have racial traits; they could just level however far they wanted.) At that time, Barbarian and Monk were class kits (subclasses/archetypes; had their own restrictions), Druid was considered to be a variant Cleric (meaning non-Humans either had access to the normal class [most] or the variant [Centaurs, Gnomes, and a few others), specialist Mages were in roughly the same boat as Druid (Gnomes could be Illusionists, but not generalists; vice-versa for Elves), and both Bard and Paladin (the two Cha-centric classes) were very nearly Human-only. Because of their human heritage, Half-Elves could be Bards and Druids, but not specialist Mages or Paladins.
This is the root of everything, I’m afraid. Note that it makes no sense with the canon about elves being musical or attuned to nature.
When 3rd edition and the Sorcerer class were in development, concept artist Todd Lockwood wanted to make Mialee (who would become the iconic Wizard) a Sorcerer, but R&D demanded Elves be Wizards. (Lockwood also petitioned for more PoC, which garnered lip service and little else; the third iconic Wizard, Nualla, is Asian and is buried on the last page of the Description chapter eight pages devoted to personality, five of which are on alignment.)
The go-to answer I’ve seen and heard (but never from an official source) for this is that Forgotten Realms canon dictated that elves practice Wizardry.
Half-Elves stayed Bards through 3.0 (racial boni on Diplomacy and Gather Information, Devis the iconic Bard was a half-elf [but you could only tell in internal artwork for the DMG], etc.). The justification was that, as progeny of two worlds, they’d have to travel (because racism, I guess). 3.5 replaced Devis (also pushed to the Description not-a-chapter) with Gimble, but the racial skill bonuses kinda sealed the assignment.
...and no one really questioned it from that point. Cultural inertia took over; an Eladrin serves as the splash art Wizard in 4e, Pathfinder gave Elves an Int bonus (and made them aliens) and Gnomes a Cha bonus (and made them expats from Faerie), and now we are where we are.
Of note: the Feytouched race (Fiend Folio, very late 3.0) is pretty much a fork of the 2e Elf racial traits; it gets a Cha bump. When I play elves in games, I pester the DMs to let me play a modified Feytouched (+elf senses tingling, +[cold] iron vulnerability, maybe -charm person 1/day).