I agree that the idea of combining steel and sorcery is popular, that’s why we keep seeing attempts to make such a class. But the reason none of them have had staying power is that they don’t have much of an identity beyond just using weapons/armor and also casting spells. To make a Gish with longevity, it needs an archetype. It needs to answer not just how the character plays, but who the character is.
Most of the better attempts at the class build the story around a special relationship with the weapon itself: it's never just a sword, the sword is somehow magical in and of itself and the character's magic flows both from and through it.
OTOH, it's not like the concept
needs a class, really. Aside from 'need' being a silly word to use in game design conversations, darn near any of the stories we'd want to tell fit within the umbrellas of existing classes, or at least could with a little tweaking. The problem is story and mechanics are not the same thing, and mechanics matter. Especially since at least 1/3 of classes, according to Defcon, don't need stories anyways, because they have tradition on their side (and the tradition for AHC is apparently "we'll do it badly as a non-core option.")
The story of an Eldritch Knight is fine, but the class, when you play it, doesn't live up to the story.
My own hot take it that this is because the wizard spell list does not, and can not, do a good job covering a totally different playstyle (specifically the one being imposed by the fighter chassis.) If paladins were told to use the cleric spell list, they would be an unsatisfying class as well, because without smites a paladin
isn't any different from a fighter/cleric multiclass with a lot of extra fluff.
If subclasses aren't allowed to have their own spell list, you'll never get a
satisfying AHC. Whereas a new class class could easily absorb all the unpopular attempts.