Of course, this could always be explained by the distances involved and the limitations of light speed, but that would make the Dark Forest hypothesis redundant as an explanation as to why we haven't yet detected any alien civilisation(s).
Even if they destroy them within say a thousand years, then at any given time there would be only few civilizations at the right age to be broadcasting. And not very loud at that.
We listen only to a miniscule portion of the Galaxy. IMO, Fermi's question shouldn't be "Why can't we hear the few civs that are close to our level".
It should be "How come we don't detect Kardashev >2 civs collonizing most of the galaxy?" Why can't we detect a single Dyson Sphere?
(I don't consider dark forest explanation to be probable though.)
Or how do we know that we, humans, aren't the colonists? Well, all the life we know comes from the same ancestry, including us.
Protector[0] by Larry Niven
David Weber's Dahak trilogy, available as the Empire from the Ashes[1] omnibus
Because most civilizations are probably still a 100+ light years apart and we just haven't been around and listening for that long? Even if we've theoretically had the chance to detect another early civilization the other listeners have been listening for aeons longer than us and are much better at it.
And 2000 years is nothing timewise on scale of universe. Plus we talk about signal that can maybe travel few hundred / a thousand light years before they blend into galactic and intergalactic noise.