That's the wrong question. It makes an incorrect presumption; Why should we have heard them? Do you think a highly advanced civilization is going to be using something as archaic as "radio signals" to communicate across vast interstellar distances? Due to the inverse square law, it's incredibly inefficient, laughably so. It would be like trying to use smoke signals to communicate across oceans. A beam of light would be more efficient. But the beam would be instant and you could never "listen in" unless you were physically at the location of the target.A "beam of light" is governed by the inverse-square law every bit as much as
radio signals are, both being propagating electromagnetic waves. It might be
"laughably inefficient" (compared to what, though?), but it seems to be what
we're stuck with. "Perhaps advanced civilisations use magic to communicate",
is what you're basically suggesting. Well, maybe they do. Ultimately, we can
only search for ETIs with the physics we actually know.
So, you're right to say that Fermi's "paradox" (always a bit of a misnomer)
doesn't prove the nonexistence of ETIs, but you can't wave away
fundamental physics because it gives an uncomfortable answer, either.
I also wanted to note in passing that it's a bit funny to obsess about
efficiency and then throw out a statement like "maybe they communicate with
gravitational waves". The state of the art gravitational wave detectors are
targeted at finding signals generated by the merging of pairs of
supermassive black holes at cosmological distances, and possibly neutron
star or black hole mergers at galactic ones. If a civilisation is capable of
smashing black holes together to send signals out a few megaparsecs, I would
submit that efficiency is the very last of their considerations. Gravity is
much, much weaker than electromagnetism.
Indeed, there are a lot of reasons to think that radiofrequency
communication would be preferred. The galaxy is largely transparent to
radiation at the hydrogen hyperfine transition at 21cm, a very useful way to
cut through the crap and dust of the interstellar medium. By contrast, at
optical frequencies the extinction from our environs to the galactic centre
is about thirty-five magnitudes, roughly a loss of 10^14 in signal power.
Radio receivers are relatively inexpensive and cheap to make and operate.
The Arecibo dish itself could communicate with a similar setup thousands of
parsecs away. Probably more now, after the receiver upgrades from a few
years back.
But you're right that we shouldn't focus on radio communication with ETIs to
the exclusion of everything else. Some folks have been discussing "optical
SETI", looking for laser/maser signals whilst piggybacking on other
observations. The SETI folks aren't stupid. But they're not well-funded,
either, and they do what they can.
They're not like radio waves where you can listen in. That's actually the
very reason why they're so inefficient, they're broadcast omnidirectional
and that takes a lot of power - wasted power.
Radio dishes are not in any sense omnidirectional. They have a beam pattern
which dictates the sensitivity of the instrument as a function of distance
off-axis. You're right that broadcasting an omnidirectional signal would be
a tremendous waste of power, which is why no one does that when sending
signals over great distances.