Putting those words over Krile's appearance seems like a misdirection to me, since the voice that said it (and the bound by duty line that follows) belongs to Yugiri, which would seem to suggest she's talking about Gosetsu.
I get the sense that Varis is being pragmatic here (if he's not being manipulated into this by Elidibus) - the Empire's previous attempts at ridding Hydaelyn of the Eikon threat have not exactly worked out the way they wanted, and here is the WoL doing a rather good job (usually) of it without needing to drop small moons on anyone or risk lives and resources to eradicate groups of beast tribes or subjugate nations. With the potential threat of further rebellion (a concern that, although not necessarily an actual threat, is one that has been actively cultivated by the Shinobi, as mentioned by Yugiri) in other provinces, engaging in further resource intensive campaigns is ultimately less attractive than seeking an alliance with the most effective "primal problem solver" currently on Hydaelyn.
There are, of course, possible ulterior motives at play - if he is in fact being manipulated into it by Elidibus, then it could be the start of putting us into position for some greater nefarious goal (using us as the template for more resonant springs to mind, or fostering a situation than can be twisted into a betrayal, and thus more conflict, playing right into the hands of what the Ascians generally want as they seek to weaken Hydaelyn and break the boundaries between the Source and the other worlds).
And then there's always the possibility (as was partially the case with Solus) that he legitimately wants the Eikon threat dealt with because it's not good for Hydaelyn...but I'm still curious about his motives here. With Solus, his ambition to conquer beyond Ilsabard predated his drive to eradicate the Eikons (and I don't trust the idea that the latter goal wholly replaced the former goal). It was in the course of conquering Othard that he first saw the havoc such a being could wreak, and it was then that it became an important part of their overall goals.
With Varis, while he has professed a similar goal (with similarly ruthless methods, as we saw in HW with Bismarck and the Vundu/Gundu situation), I don't know if we know if he holds the same "must conquer" ambition that Solus held. Basically, is the goal to remove the Eikon threat just for the good of the planet, or is it also to remove a major obstacle to further expansion?