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.
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.
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].
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.
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. 
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.