My argument for Dracthyr Shaman would be as follows:
At least, as I understand it, Dragons are aspects of nature/life which includes the elements to some degree, with Blue have Cold Breath weapon attacks in addition to managing the Arcane Energy of Azeroth, Red having Fire Breath Weapon attacks and managing Life on Azeroth, Bronze having Sandy Breath Attacks and managing Time, Green Managing the Emerald Dream (Another tie to Druid here) and also being a different aspect of life with poison breath attacks, and Black having fire breath attacks and managing Azeroth/The Earth itself.
It would appear to me, as Dracthyr as I understand are hybrids built from all 5 dragonflights, that the “elements” pun intended are there to support a Shaman Class Fantasy and connection to the spirits through both breath weapon attacks and the aspect connection to the elements and to Azeroth on the whole. I feel as though they would make compelling Shamans with unique totems in combat, easily able to support Enhance (I mean, Augmentation Evoker is kind of enhancing with Dragon Elements), Elemental (Again fire and earth attacks, lightning isn’t too much of a stretch) especially with Devastation being similar, and of course Preservation being Life and nature we are easily seeing a correlation to Restoration Shaman.
Not to mention this would give Alliance another playable Shaman race option in addition to the pre-existing option for Horde players to pick from.
I think Shaman should be playable by Dracthyr.
Now as for Druids, again as explained above, which I will not rehash for the sake of brevity, we see a connection to the natural world, to nature, to preserving life and balance in many of the Aspects (Red, Green, Bronze for Time, Arcane for Blue, the Earth itself for Black) that Druid feels like a no brainer.
We could get special Dragon animal forms similar, but different, to the Zandalari Druid forms that are most similar to Dinosaurs. Flight Form may even simply be base dracthyr dragonflight mode. You simply become your own dragon self and dragonfly.
Guardian could be a tanky full dragon form, but of course smaller for visibility sake, something like a Drake form with wings and claw attacks and such.
Travel Form on the ground could be the 4 legged Drakonids or some other draconic form associated with speed.
Balance could be the Standard caster form, Moonkin, or a modified Dracthyr form similar to the Zandalari dinosuar caster form.
This would introduce the FULL playable Dragon aspect in some way to the game that players, I think, crave to some degree, and would offer both HORDE and ALLIANCE a new druid race that keeps Druid Parity (so one side isn’t getting while the other is).
I think playable Dracthyr Druids should be a player option.
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