Hey Critkeeper! Thanks for your analysis :)
Your post is a bit of a long one but it's on my favorite topic in LoL, so I'm going to give it a similarly detailed response. But I'm just sitting at work spitballing, so it will be a bit scattered, and there's a chance I'll make some silly mistakes or say something that's only partially true or leave out something cool I'll wish I'd elaborated on, so I hope you don't mind! But the TL;DR is that you're pretty spot on that we haven't reached full role-item array saturation. Whether or not full saturation is a good or a necessary thing is a bit harder to say, but let's start from the assumption that it is (this aligns with my personal beliefs).
When LoL started, class distinctions were very blunt and vague: AD carry, AP carry, tank, bruiser, support. As such, the items were relatively imprecise: did you want AD, AP, tanky stats, or team-assisting actives. I believe the first real distinction that started getting made - itemization-wise - was with melee champions.
People used to get into arguments over what a "tank" was all the time. One set of people just said tanks were any champions who built tanky. Back then, people would call Dr. Mundo and Jarvan and Nautilus all tanks. It was an imprecise world. The other side was saying that there were two types of tanky champions.
One class of "tanky" champions was gold hungry; they built the exodia build of Warmog's Atma's Trinity Force and scaled pretty well, to the degree that they became one of the most frustrating classes in the game. Soon, the name "bruiser" stuck.
This stood in stark contrast to "tanks" could build nothing but gold items and still do well. Of course, it was actually even more complicated than that because junglers like Mundo and Shyvana would build jungle items and build tanky AD.
The other contrast was ADCs; you basically had two classes of ADCs; BT first and IE first champions.
Fast forward a season and you get Black Cleaver and the Youmuu's rework and people started to realize that AD Assassins were a class that had just needed items to function. We stopped calling AP Assassins at some point and started calling them burst mages because AP Assassins tend to have CC while AD assassins don't.
To avoid this being a lengthy history lesson, over the last 12-months or so, Juggernauts got their items, and then ADCs got their itemization rework, and then there was Mage Update.
We've been working on the class list behind the scenes, and as you can guess from those three updates, plus the upcoming assassin update, one of the big initiatives at Riot is updating each class to have a clear identity. A lot of things determine what classes get updates.
Juggernauts got theirs because they were probably the least supported class in LoL. We just overweighted them with stats because the game systems didn't allow them to function.
Marksmen got theirs because the class was relatively indistinct. You mostly just picked one of the marksmen that was strong at the time because they were so similar that style rarely mattered.
Assassins, on the other hand, are getting their update because they're one of the most frustrating classes to play against, so there's a huge impact on live to their existence.
When we update a class, we typically want to hit three things: kits, items, and systems. For example, with juggernauts that looked like this:
Kits - Removing excess mobility, changing scalings,
Items - making more mobility items, introducing items to match those scalings.
And that leaves systems. What do I mean by "systems"?
You'll note that many juggernauts scale with Base AD (rather than Bonus) and Health. This is intended, and allows us to tailor items to them by loading them with those stats. But here's the problem. When we reworked juggernauts, we didn't also rework every other champion. There are plenty of other champions with Base AD or health scaling, and those champions also love the juggernaut items. Given that those items are overloaded at their goal of filling the weaknesses of the juggernaut class, they often ended up heightening the strengths of champions who could take those items without having those weaknesses. For example, Darius needs Dead Man's Plate to chase most champions down. But if a champion like Jarvan can take that item efficiently, he can just chase you down with all of his gap-closers. And while Titanic Hydra is aimed at juggernauts, other melee champions who like Base AD and health can grab that and go on to also build damage and be this weird tanky never-dying champion who can still one-shot you (Fiora got pretty scary for awhile there)
Artillery champions benefit highly from regular AP items, and it's quite likely that the reverse would be true. And so it requires a good deal more care to make sure we don't accidentally make it impossible to balance all other mages just to give Artillery champions their items. Or it may even turn out that Artillery champions don't have differing itemization needs from generic mage items because their class already hits its niche so hard. Same goes for skirmisher.
I hope this gives some context: you're definitely right that those classes don't currently have class-specific items. It's a bit harder to say whether that's a problem. It's even harder to turn that problem into a design solution, especially when there are more pressing - or more easily solved - problems nearby for us to tackle.