I think a more practical take on this isn't life is rare it's that both space and time are big. Two civilizations existing simultaneously but 1/100th a galaxy apart are still a thousand light years apart. Each would see the other's home system as one of billions of observation candidates.
Even with massive SETI operations by both civilizations the odds of those two civilizations discovering one another are pretty small. Even if we posit advanced civilizations are more abundant, separated by only a few hundred light years, the odds are still very small any two civilizations will find each other.
Detecting "leaked" radio emissions just isn't a thing that can happen. The inverse square law make this plain. If we placed our most sensitive radio telescopes on a planet in the Alpha Centauri system we wouldn't be able to detect Earth's radio emissions save for rare blips where a powerful radar system's beam happened to point directly at Alpha Centauri. Earth would need a system of persistent ASETI transmitters aimed at specific stars to have a chance to have emissions be detected by civilizations there.
There don't need to really posit anything weirder than space is fucking huge to explain the Fermi paradox.