Would we hear it even with simple on/off keyed modulation even? The distances are so vast that even a directional link with anything but our nearest neighborhood seems unfeasible. We should have met a von neuman probe though.

Or possibly advanced civilizations had the same realization that many scifi authors have had about such probes. Something goes wrong and they cause widespread destruction. Or they work fine but still end up causing widespread destruction simply by replicating.

Once it happens once, it's too late for everybody. Naturally, they evolve, and soon invent interstellar travel. So much for that galaxy.

(Cue Fed Saberhagen, *Berserkers".)