Pretty sure it's easily refutable.
1e and 2e required both Enchant an Item and Permanency, both enchantment spells.
3e required the spells listed in the magic item itself and minimum spell levels. Transmutation was not required.
4e dunno.
5e Up to the DM, but nothing says it needs transmutation.
Yeeeeah, 'cept no.
For starters, Enchant an Item, in the 1e PHB, is a Conjuration spell...actually, in print, as "Conjuration/Summoning." Permanency (as makes complete sense) is listed as "Alteration." Which, I am sure a scholar of your caliber is aware, in 2e the school was made "Alteration/Transmutation," as most (if not everything but Necro, I think) was "double" named: "Illusion/Phantasm," "Conjuration/Summoning", and so on.
But thanks for asserting the misinformation with such sureity.
I am not suggesting that 5e, or any other edition, SAYS this is what it is. But Transmutation, not Enchantment (regardless of the "Name/Title" of the spell), is the magic which changes things. Not just literal "form/shapechanging." The magic to make "something" into "something else" is Transmutation, whether that is "visible" or "physical" is not really relevant...though, clearly, those types of spells are obviously transmutation as well.
The other thing that the game has not always been great with, but is definitely presented in places since 1e, is that many many spells are NOT solely a single school.
My point was, the generally vague "rules/rulings/suggestions" for "enchanting items," is like the structure of a computer program. You can have circles within circles, within four dimensional shapes... abjuration runes traced inside an illusion triangle wrapped in a transmutation square. When you "close" that program and "run" it (in a neverending repeating loop, i.e. Permanency), you have a cloak of invisibility.
The combinations of "magic words" and "magic gestures" and practices and forms, sigils and glyphs and runes and diagrams, in infinite combinations.
Some do what you want. Some will do what you don't want. Some done wrong or mistakes made can be catastrophic or result in nothing happening at all.
In any and all cases, what is this "program" or wrapped up package of magic doing? Changing the item into something else. Giving it different properties. Making it resistant to damages. "Adhering" magical effects, and thus their auras, to the item, permanently (though I'm sure ways could be devised in the creation process to mask an item's powers/magics).
At its core, you are changing the nature and properties of the item. That = Transmutation...and all of the individual separate effects (of any number of schools) being contained in the program or gift box or "onion" of the item...pick your preferred analogy.