But that's the whole point.
If ants could talk and they asked why this massive being was killing them all with poison, and the exterminator's response about how this is his job, that the ants are nothing but pests to beings like him, how is that not still an Cthulhu-esque horror to the ants living in the hive? It's about being cosmically insignificant.
Now I do admit that the Sovereign was a bit too malicious in his talking down to Shepard, (like a kid with a magnifying glass, taking perverse joy out of frying the ants) but his talking to Shepard in an of itself doesn't detract from the Lovecraftian elements.
As dreamgazer says, it's giving them signifance. But it's more than just giving them significance - it's creating a basic shared frame of moral reference. If ants could talk to us and we could understand them (and they could understand us!) then they stop being pests, and it's starts to be a genocide.
Giving the reapers lines moves them from Cthulu-like to space Hitler with superpowers.
An "externinator" IRL doesn't think of ants as people. But the very basic premise of your analogy turns ants into people by endowing them with the most foundational abilities we associate exclusively with humans: speech and sapience.
The whole point of Cthulu-like is that there is no frame of reference. There's no concept we have that even allows for an analogy. Things happen as if they were natural phenomenon embodied in a thing we identify as somehow having agency.
The very fact this is a thing you can kill at all forever removes this quality - because we understand death just fine, and killing Cthulu is a contradiction.