I'm not sure why a bard would be a mystic class, or nature magic focused.
Aside from it beginning that way in the game? Historic or at least mythological accounts of Bards' abilities, and the cultures the archetype stems from (primarily celtic, germanic, and nordic) all point to a more "primal"/Nature magic type of magic-wielder.
Someone who sings or chants their magic into creation, who "calls upon" the magic to happen.
The Arcane caster with full spell progression D&D has made of it is definitely not my flavor/take of what a Bard is, was, or should be.
And warlocks don't channel magic -- they are taught secrets no mortals are meant to know. they are still "wizards" but without any of that pesky studying.
[EDIT: Sorry missed this in the initial response and totally intended to respond to it.]
Warlocks, from where I'm sitting and flavoring, absolutely "channel magic." They are being GIVEN the energy and know-how from their "Patron." They are "imbued" with magical power...not something of their own. Much more like a Cleric. Much more like a Druid. To my mind, than person who learns/figures it out on their own.
It comes down to "what is "Magic" and the various "types" of Magic? Why aren't healing or "speak with animals" spells on the Arcane spell lists? Why isn't (traditionally) "fireball" or "fly" on the Divine magic lists? Are they just arbitrary labels for supernatural things from legends and literature? Or are they actual different FORCES/ENERGIES that are transmitted/accessed/harnessed and released using DIFFERENT methods.
A Cleric is IMBUED with their power by the god/gods...through their devotion and faith and all of that...but it is GRANTED power. Not something they master or access themselves. For me, warlocks are exactly the same...just not receiving power from "gods."
That is, for me, all a warlock is/ever will be. They are the "cheaters" of Arcane magic. Given their abilities, rather than having to practice and master them. Shown how to access them....and capable of repeating an incantation and getting the gestures right (because their PATRON gave them that) to make "the things that wizards make" happen.
But warlocks don't function out of some supernatural understanding/unraveling of the cosmos or innate talent or inbred power (if one likes their wizard/magic-users defined that way) or hard-pressed intellect containing multitudes mastering the unfathomable. They function because their PATRON wills it, gives it to them, and makes/allows it happen.
That's what the modern understanding of D&D Warlocks do. They are
beholden, and (if in my game at all) will be forced into a consequential "pact," not just some background or story element that means nothing in play with the warlock not being accountable to anyone for anything.
[/EDIT]
So, neither. Make an elemental bender instead.
"Avatar the Last Airbender" with the numbers filed off is not really of interest to me. Though I do have Elementalist specific wizards intended for a supplemental.
But thanks for your input.
PS: Why does everyone separate the cleric and druid?
Because worshiping and calling upon gods/deities, as specific personalities, to conduct your "divine rites and magics" is not really the same, again as my tastes and expectations and knowledge of the class -both myth/legend/literary and as presented in D&D- as what druids do.
It has taken FAR too many editions of the game to understand and present "Divine" magic/spells and "Nature" magic/spells as the very different things and themes they are (and have been for my homebrew world for quite a long time).