I think that scenario would imply a relative scarcity of intelligent life: after all, if a space-faring civilization needs to transmit powerful, omnidirectional signals in the blind, it must be pretty lonely. Maybe, just maybe, the fact that we're not seeing much is actually indicative of a fairly rich sea of life in the galaxy, communicating point-to-point with each other. Not so much to randomly overhear in that world.
I am a big fan of science and science fiction, do not get me wrong. I do feel that technology evolves and will surprise even the most tech savvy, but to violate faster than light travel seems more far fetched than any theory out there to me.
At the same time, space travel technology will also have been advanced, allowing for self-sustaining spacecraft that offer protection against the harsh environment of outer space.
At that point, you can imagine that a hearty band of explorers will undertake a mission of leaving our solar system and exploring way beyond our world. Who knows how far they could get.
These are the sorts of advances I can imagine becoming real many generations from now. I wouldn't underestimate our capacity to make it happen.
Both our bodies and minds need to hardened to endure deep space.
10,000 years between stars is a long time to be playing solitaire. The voyagers may need to sleep, hibernate, slow down their metabolism, alter their perception of time, or something, to make the journey bearable.
At least someone in the universe would be living out my space opera fantasies!
L = 20 * log10(4 * pi * d / λ)
If I'm doing the math right[2], this says that the path loss over 1 lightyear for an 80MHz transmission (which seems to be in the analog TV range?) is something like 330 decibels. Now I'm not sure how strong TV transmissions are, but I'm guessing it's not that strong.
Darn. Seems Futurama and every other piece of mass media that claims that aliens are watching our TV from 80 years ago is wrong.
[1]: https://en.wikipedia.org/wiki/Path_loss
[2] Which is to say, if I'm typing it into Wolfram Alpha correctly.
Except for the small question of how those many civilizations would have found each other in the first place.
It's not very likely though. Occam's Razor alone suggests that the reason for loneliness is that there aren't a plethora of civilizations all talking to each other over narrowband channels. And we'd be very unlikely to pick up the omnidirectional beacon of a lonely civilization way out here anyway.