As to the Half-Caster, its not just symmetry, its (yet another) repeating thread. The Gish is missing. I've looked at and compared the 5e options, none of them hold a candle to the PF1 Magus.
The Magus is something much better-designed and more bizarre than just some generic "arcane half-caster" though, at least in PF2. Its reason to exist (at least as of PF2) isn't to mindlessly fill an "arcane half-caster" slot but to be something more peculiar and specific.
As for a Gish, I kind of agree, but I also don't think automatically selecting arcane half-caster is the right way to go. If 5E's MCing rules weren't 3E-style junk/dual-classing, this wouldn't even be an issue. I suspect a genuinely good Gish for 5E wouldn't be a half-caster at all, but more like the Warlock chassis with some tweaks.
It's spells designed for the class.
The key problem with the Artificer, AT, and EK in 5e is that they don't really have their own spells.
The Paladin and Ranger , due to the iconic status, will get book space in the PHB for both spells designed for the class and class features designed to meld with divine/primal magicand their weapons.
This is why the arcane half caster can't be in the PHB. It won't get the book space.
This seems like the fetish continued. You're putting the cart before the horse.
You're saying "we need an arcane half-caster" not "I have a great, specific and detailed idea for a class that would be really compelling, I guess they would probably be an arcane half-caster".
My point, in the end, is that this "cart first" deal is a fundamentally bad way to approach game design. You don't create a class for the sake of symmetry. You create a class because the class justifies it's own existence. If you decide to fill in "gaps" you often end up with pointless and ill-conceived classes. Even 4E, which did extremely well with the power source/role thing had a few classes which didn't really justify their own existence.
I do appreciate your point re: needing class-specific spells, but honest that's not what makes the Paladin or Ranger. Even if both had no class-specific spells they'd be about as good and flavourful as they are - and I bet an arcane half-caster would mostly be spamming Shield and a few other spells.