Tainted sprites, sure, but tainted elementals?

[Valence]

I recently got a random thought. We have many series of quests around the Twelveswood where it's about curing taint from various ailments and sources (conjurer story quest, gridania starting MSQ, white mage 50-60 quest...) that seem to pervert and turn nature into various monstruosities, Chernobyl style. 

 

But... do we have clues in the lore if a similar fate could happen to elementals themselves, or are they just immune to every taint with their Succor and all? Is the worst that could happen to be them going mad when balance is broken, or just getting destroyed as when the Ixali try to kill the ancient tree as part of the MSQ? 

 

By the way, can they even be eradicated? How do you kill them exactly? What were those Ixali trying to achieve in retrospect by killing a huge tree?