It's likely already been suggested a dozen times, but I'll throw it in again.
I was playing with my battle pets earlier, and found Doom Bloom; a hydra that is made of plant material. I then remembered that there were a bunch of hydras in Draenor that were MISLABELED as Elemental, so I checked Wowhead for the fun of it to see if there were any with correct classification. Lo and behold, a whole bunch of "Mandragora" enemies were labeled as tameable! I jumped for joy as I rushed out to Shadowmoon Valley, Gorgrond, and Spires of Arak, hoping to just tame any one of them. Alas, all the ones labeled on Wowhead as tameable were still Elemental, but I tried Tame Beast anyway in hopes that it would still work. Sadly, they STILL can't be tamed for whatever reason.
Please, make the plant hydras tameable. Animals move, not plants; they should be beasts.
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Name the game these characters are from, and I'll be amazed.