"even planet-killer tech isn't an extinction-level event."
We're talking about probabilities.
You're right that a civilization that has violent tendencies may not self-destruct since it may turn out that the destructive potential of future technology is confined to the capacity of city-scale destruction instead of solar-system-scale destruction. Or they may escape their host planet quickly and diversify before nukes or whatever comes after nukes wipes them out.
But it seems to me that the probability of extinction is non-trivially positively correlated with violent and tribal tendencies once that civilization reaches our stage of development. And so that nudges the odds towards an advanced alien civilization being peaceful.
"Over thousands, or millions of years"
Yeah, over a million years, which is not much on cosmic timescales. If FTL travel isn't possible, it'll take many millions of years to go anywhere.
I believe it won't end up as a vestigial organ and will be actively selected against. Tribal conflict has a positive reward to the victor in a resource constrained environment but is negative sum over both parties. Without the payoff to the victor then all we are left with is a negative sum outcome which should be selected against. The only thing I'm not sure of is tribal conflict over reproductive capital, although I can imagine that technology could make that abundant as well.