"Divine" magic and "Arcane" magic are stupid separations that make absolutely no sense with the number and types of classes we have in 5E. There, I said it.
What we should really be talking about here is simply "Cleric" magic, and "Wizard" magic. That's it. Why? Because none of the other classes do anything that makes them fit into either the "divine" or "arcane" divisions, and those that try to do so have to make stuff up to put them in.
Neither Druid nor Ranger spells are "divine", because neither of them come from any gods. They come from what... nature and the earth itself? That's not "divine". In fact, they're both closer to "Arcane", because "Arcane" is just the magic in the air, or "The Weave" or "The Force" or whatever it is on the Prime plane people tap into. So what's the difference between the magic in the air and the magic in nature? Damned if I know.
Similarly... Warlocks are NOT "Arcane". They are given their magical power from extraplanar entities the same way Cleric are given theirs (other than bargaining for it as opposed to working for it). Yes, the clerics entities are "gods" and the warlocks are "archdevils" or "archfey" or whatever... but what is ostensibly the difference between those groups? Very little if you ask me (especially if you are talking about sheer power). So Warlocks are "divine" casters if anything-- much moreso than Druids are-- especially for the so-called "Celestial" patrons! Warlocks bargain for their power from the immediate underlings of the gods, and yet somehow their magic is still supposed to be "Arcane" in nature? Really?
And what about Bards? Where do they fall? Are they "divine"? Apparently not. Are they "Arcane"? Doesn't seem so (if the pack of Arcane Spell Cards that WotC released through Gale Force 9 had anything to say about it.) So what kind of magic do Bards produce? What's the point of having two categories if there's a whole bunch that don't fit in either and you don't bother placing them anywhere else?
None of the divisions of types of magic make any sense whatsoever, so using them I feel is ridiculous. There is just "Magic". And "magic" is anything supernatural that normal people cannot do-- whether that be spells, or invocations, or ki, or metamagic, or channeling divinity, or bardic inspiration, or divine smite, or wildshaping, or beast mastery, or any of that stuff. It's all magic. And everyone gains magic and uses magic in their own particular way. No categorization required or necessary.
The two separations per the PHB indicate direct access to magic versus an intermediary connection to magic. From what I read in the sidebar it is just one magic and the classes have different ways of applying it.
I'm more a fan of just calling it cleric magic or bard magic or wizard magic etc too. Additional labelling does nothing but add additional labels for the sake of adding additional labels.
I'll comment on the cleric vs warlock, however. The rules for arcane vs divine means clerics need that connection to access the weave. Warlocks do not, which is why it's arcane. I interpret that to mean the patronage requires a one-time or irregular rituals in the leveling up and learning process for warlocks that permanently empowers the warlock to use magic directly where the clerics do not have that same option.
Warlocks using an arcane focus instead of a holy symbol reinforces that distinction.
It's easy enough to rationalize based on the way arcane and divine magic is described. The spells aren't actually arcane or divine but the manipulation process is. It's still unnecessary but seems to be a legacy inclusion.
FWIW, the sidebar on PHB pg 205 states that Wizards, Warlocks, Sorcerers, and Bards use arcane magic. Clerics, druids, paladins, and rangers use divine magic.
Although, personally, I've always liked the idea that there is just magic. That opens up priests who don't receive their power from a divine entity, but rather are simply learned (or gifted) men and women. I think that would offer some interesting potential for adventures (a priest who is creating 'miracles' - is he a con artist or is this the work of an unknown entity?).
That's an important consideration for how Eberron is handled given the "gods don't interfere" concept. Gods who may or may not exist and do not communicate with followers or directly grant magic but gods are granting magic? I call "nuh-uh", lol.
Heh heh... well, it's still dumb, because there is literally nothing about druid magic that is any more "divine" than warlock magic, and in fact the opposite is true.
That page also says nothing whatsoever about Monk magic (Four Elements). I guess we're supposed to assume they are divine as well... but seeing as how there's like little to no difference between an air-based Monk and a Storm Sorcerer (they are both drawing energy from the air around them to create their effects), calling those Monks divine makes no sense either.
When Clerics and Wizards were the only thing in the game... having divine and arcane magic as descriptors made sense. But not anymore. Not in 5E.
Based on how "The Magic of Ki" is described monks would be arcane casters when casting spells because they are using ki to power it. The actual spells they access follows the arcane caster style as well. Or a person can stick with a class as the type of magic (which makes more sense, I agree).
Bards are not actually listed as arcane casters in the bard class description either even though divine and arcane reference exist in the classes for clerics, druids, sorcerers, warlocks, and wizards. Bard magic gets described as hidden magic and the cannot use an arcane spell focus. But they still get included with arcane casters but the only thing that really shows that is the sidebar including them in that list.
What I find interesting is if a DM enforces the old school "divine casters cut off from their divine link cannot recover spell slots" then clerics, druids, and rangers suck getting into planar travel compared to artificers, bards, and divine souls regardless of a lot of shared spells available.
Personally, I think arcane vs divine labels (and others) is an unnecessary addition that adds complexity if it ever gets used beyond fluff. I agree with your assessment.
