Your argument has multiple fallacies and makes assumptions that may not hold.

- Anthropocentrism and convergent evolution. Why should extraterrestrial civilizations resemble ours in any way? Their neural architecture, senses, communication methods, technology, culture, and prime directives could be as unrecognizable to a human as humans' to a fruit fly. Maybe they evolved on a planet bathed in radiation from numerous sources and have sense organs that allow them to communicate with each other by transmitting and receiving X-rays. What if this radiation prevented them from making accurate astronomical observations beyond their planet, thereby severely limiting their scientific progress? Or what if the particular operation of their brains makes them completely disinterested in space exploration? We can't rule anything out. On a related note, you seem to assume that the development and use of specific technologies for broadcasting signals to the universe is inevitable for any intelligent civilization. There's no reason to suppose that. Aliens could be using different bandwidths than we do, or a different technology altogether.

- The cosmological timescale argument cuts both ways. We've had the technology for detecting non-visible astronomical radiation for less than a century. This is a vanishingly small window of opportunity. The last signals from an extinct civilization could've easily passed our planet eons ago - or conversely, may have yet to arrive.

- I don't think you fathom how large space really is. There could be thousands of space-faring civilizations zipping around the Milky Way, and the odds that any one encounters another during their existence overlap window would still be infinitesimally small. For all we know, a civilization near the center of the Milky Way could have developed near-light speed travel 20,000 years ago, packed their bags, and took off in our direction. If so, they've still got another 6,000 years to go (from our frame of reference). And unless their heading is reallllllyyy precise, they could easily overshoot our humble Solar System with neither civilization ever being the wiser.