Some thoughts on core 5e classes.
1) [Wizard], [Druid], [Paladin], [Monk], [Artificer] are the strongest fictional identity among the core classes. No notes. They have an obvious identity and are easily recognizable as a class within pretty much all baseline D&D settings.
I mostly agree here. Wizard gets a bit odd though. The idea of studying magic is very thematic, but it isn't as strong I think as you may think it is. Case in point, many of the most famous Wizards could be argued to not be wizards (Gandalf is a Celestial, Merlin speaks to spirits and is half-demon, Dumbledore was born with magic powers like a sorcerer) This isn't a huge point, just that I would argue Wizard is as generic as you can get for a spellcaster.
2) [Warlock] has a strong core identity, although its story is weakened somewhat since the patron can just as easily be an involuntary boon (or curse) as opposed to a proactive choice to seek power (the "normal" warlock story). When we're talking class as diegetic element, having multiple backstories lead to the same power progression isn't a virtue.
Maybe. Each warlock can be built very differently, and it could be simply a generic grouping. Kind of like how the One DnD team initially attempted to make warriors, mages, ect, the "Warlock" can be a class group, which acts as a catch-all for "patron granted magic"
3) [Sorcerer] has a strong concept, but its story is all over the place; it also doesn't have a real narrative place in core D&D settings (other than "outsider not-a-wizard"). It mostly exists as a contrast to [Wizard].
See, to me, they have just as much of a story as the wizard. And this is kind of the issue with the arcane classes. As story tropes, the three are practically interchangeable. Mechanically we can see a difference, but the stories almost feel incomplete without each other.
I think, from what you have proposed, sub-classes and class groups are the best way to resolve this. But there is always going to be overlap. A tiefling warlock who patron is their fiendish parent is going to blur that sorcerer and warlock line and may, in universe, be best expressed as unique classes.
4) [Bard] has a strong conceptual image, it also has a strong mechanical structure (in 5e), but the two don't actually mesh very well. The fact that different conceptions of [Bard]s can go from no-magic all the way to competitive with [Wizard]s makes inserting the [Bard] as a coherent diegetic element difficult.
One DnD would have fixed this. And I am still mad they removed it. I like the idea of Bard being the FIRST magic users, and that their magic, which can be found through study of the world and music and story, is the baseline all other magic riffed off of.
But, also, I think this is also fine. The bard is a flexible class, and sub-classes are where that is defined.
5) [Cleric]s are one of my major pain points for diegetic classes. Why do people who follow gods who are completely in opposition still gain 80% of the same power set? [Cleric]s work with a setting with a strong medieval church analogue, but are really problematic to explain with a pantheon like FRs.
This can be rough. Especially when you also need to ask about nature clerics vs druids.
I solved this by saying that there were no gods of nature, no gods of magic, and that the role of "evil god" was handled by the other classes of Powers. The moment it is the Gods vs the Archdevils and Archdemons and Archfey and Elder Evils then the role of the cleric becomes much more coherent.
Another thing you could do is that the System doesn't care about the gods. You worship a god? These are the powers the system gives you. After all, you don't get different sets of abilities from serving two Kings that fight, so why would you for two gods?
6) [Fighter]s and [Rogue]s are the worst. How do they stand out from the masses of "people who are kinda around", other than being, ya know, not dying quite as easily? I would take them out, or barring that, move their subclass to level 1 and attach strong narrative elements to the subclass.
The subclass is where the narrative is, but I think you are being too harsh here. A Fighter, even at level 1, is as good as any grunt in the army. They are actually very good at what they do, compared to the common baker or merchant who pretends to fight. And the Rogue is much the same way. Sure, expertise in a skill is something that can be generic, but the sneak attack and the coded language does create a narrative that the only classes don't really have. They are a bit generically "the expert" type of archetype, but by the time you hit level 2 it is solidly locked in what these people are like.
