Trying to spin up axioms and theories about the game theory of whether or not to destroy alien species seems hopeless to me. There's so many parts of it that hinge on what is or isn't possible to know and do in the first place. It could easily swing either way based on countless factors we know nothing about.

I'm far from saying for sure that something like that is definitely true, or even more likely than not. But it seems reasonably cautious to me to not arbitrarily broadcast out to the universe our location and rough technology level. We have no idea what might be out there or what its capabilities and thought patterns might be. Or rather, it seems hopelessly naive to me to just go ahead with such broadcasts, confident in our theories that nothing could possibly go wrong.

Regarding point the second point. I assume there's a cost associated with using the weapon, even if it's untraceable.

Regarding the Berserkers, it sounds a bit like a grey-goo scenario with self-replicating machines that wipe out all life. My personal feeling is that these scenarios are unlikely. If it were possible, it would have happened already... but it would be interesting to hear more systematic discussion of this point.

With my brief googling, I've found it pretty difficult to find anything on real "cosmic sociology". The research work I've found has mostly focused on human colonization of other worlds. I feel like it would make fun reading if there's anything out there.