Artificers work in most settings, as there's a place for "arcane crafter" in most official 5e settings (Theros because of Purphoros, Ravnica because of Izzet, Toril because of Lantan, Spelljammer because Mercane and Tinker Gnomes, Exandria because they're confirmed to exist there, and Greyhawk has a few historical "artificer-type" characters, like Lum and Leuk-O). And Alchemists exist in basically every D&D world. And there could be more subclasses that would help it fit in more settings (Dr. Frankenstein-style fleshstitcher for Ravenloft, Portal-based Artificer for Planescape, Runecarver for basically any setting with Giants, etc).
Hard disagree, because the vague lore doesn't match the mechanics or how they actually work at all.
The idea that the crafters from Lantan match up with Artificers for example is absolutely a joke (and yes I'm aware the book claims it, it's still nonsense).
If you banned the only actually-good subclass of Artificer (Armorer) and the mediocre ones (Artillerist, Battlesmith), and you only had the Alchemist subclass, then you might almost be able to make this argument, but not really because they're too weird in terms of real mechanics. Maybe on a really good day, if you squinted your eyes and basically reflavoured it, you could argue Battlesmith kinda sorta fit too. But it's not good. And Armorer and Artillerist are just a hard "no" for most settings. Basically Fantasy Iron Man and some dude with a gun turret following at his heels are just not fitting most settings.
More subclasses as you describe would probably just give more subclasses that wouldn't fit in most settings, because the class is fundamentally problematic.
But that's not the only problem they have by any stretch of the imagination.
1) They're not filling in a gap for a popular missing fantasy archetype. They totally fail to fill in the gunslinger gap some settings have, because the artillerist is terrible at that, even if he makes the hand-held turret. He's at by far his most powerful just ramming THP up the entire party's bums 24-7.
2) Their current design is an absolute disaster.
Unlike all the other 5E classes, which cluster in the like 68%-100% effective range, and stay in that cluster even with really basic/bad optimization by players, Artificers rely extremely heavily on system mastery, and indeed knowledge most players shouldn't really have and more importantly - don't have (like, a detailed understanding of all magic items). With their weird way of doing things, the difference between good spell selection and ability selection and disastrously bad is absolutely huge. And the subclasses vary insanely in power, with the Alchemist being pretty trash, and the Armorer potentially being extremely powerful if you know what you're doing.
As for system mastery, unless you pick the right spells, and the right effects and magic item effects from your infusions and so on, you're absolutely stuffed, but if you do, they can shine very brightly. They're not remotely balanced or anywhere near equal. And it's extremely complicated and absolutely full of "trap" options and mistakes you can make that will ensure you're a mediocre performer at best.
You know how some MMOs have difficulty ratings for the classes? Well, if D&D 5E had them, none would be above three stars out of five, except Artificer, which would be five out of five maximum difficulty.