The problem we have always had with the idea of a arcane half-caster is that no one (even people who have tried creating their own) has been able to come up with the most important part of the class-- its story.
That's why no arcane half-caster has ever survived or ingrained itself in the collective D&D consciousness to become an actual "thing"... no one has created a thematic story for the class that puts in on par with the ranger and the paladin. There hasn't been anything for this class to hang its hat on.
I mean, what are the stories of these three classes in D&D?
The paladin is a divine half-caster, but is also a knight, a templar, a holy warrior that swears to uphold certain ideals that society finds important. They are the champions and defenders of society.
The ranger is a primal half-caster, but also a wilderness warrior, a defender of the wilds, a champion of nature that moves swiftly through it to protect it from those that would use it for nefarious deeds.
The arcane half-caster? It's a fighter that casts spells.
Yep. That's it. That has always been the "story" that people have created for the arcane half-caster. That's what an eldritch knight is. That's what a swordmage was. That's all it's ever been. And that's why no one and no edition has ever stuck with it as a class. Because it has no story, no theme, nothing to give it any heft. Nothing to make it a CLASS rather than just a multiclass of two generic classes smushed together.
If we ever want to see an arcane half-caster be a thing and become an actual class that remains in the game... we need to all agree on what its story is. Who in medieval D&D society needs to be a warrior who casts wizard spells? What do they do? What is their duty in the world? What do they believe in and fight for? And whatever it is... it needs to be an actual specific type of person on par with the ranger and the paladin. One who theme is so strong that it can support multiple variants of its story that come into play via subclasses.
The fighter, rogue, cleric, and wizard are the only four classes that get away with being somewhat "generic". But the other eight have major story, lore, and fluff connected to them. Barbarians, bards, druids, monks, paladins, rangers, sorcerers, and warlocks are just covered in fluff, and that's why they've stayed in the game. Because they are specific archetypes that the game and its players have determined they WANT to have available, moreso than just making multiclasses.
Could the game work with just a fighter/cleric multiclass for their holy warrior archetype? Sure... but people want PALADINS.
Could the game work with just a fighter/druid multiclass for their wilderness defender? Sure... but people want RANGERS.
Could the game work with just a fighter/wizard multiclass? It always has. But if you want an actual class for it now... then we need to come up with WHAT IT IS.