[b]When Tlaloc's Exotic Perk is Active, it should gain elemental damage matching your Subclass.[/b]
This makes sense Story-wise, since the Overflow perk is using the Warlock's Light to power the gun.
And since the weapon is all about trading your super, it seems fair that you should be able to use it for elemental damage your super would have done.
Also, we need more Exotic Elemental Primaries other than Zhalo Supercell, and this seems like a good place to start.
p.s. You know how Bishop from X-Men can channel energy into his gun? Same idea.
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And this is why bungie gave you susanoo...