On the other hand, based on our own experience, broadcasting radio signals is a waste of energy and bandwidth, so it is likely an intelligent society would quickly move to low-power, focused transmissions (e.g. cellular networks or WiFi). Thus the radio "signature" they broadcast to the universe would peak for a few centuries at most before dying down as they figure out how to shut down the "leaks". That would explain why we observe nothing, if intelligent societies do exist in the vicinity. Of course, these societies might also evolve rapidly soon after, perhaps go through some kind of singularity, and might lose interest for "lower life forms" -- which would then explain why they might not look for our signals or leave them unanswered if they listen for them.
Now that is a good argument that doesn't miss the point. My priors would say it's not even "a few centuries" - I'd expect less than one earth-century on average, with most of the variance due to the particular economic variations and social phenomena derived from the details of the species.
"The Planet-of-the-Apes Hypothesis" Revisited --Will Intelligence be a Constant in the Universe?