I always found the Fermi paradox too non-paradoxical.
If the closest aliens are in Andromeda, we can't
pick out their radio signals, and we might never be able to. Yet it would still mean there are an insane number of alien civilizations in the universe, counting in hundreds of billions. So even if the universe is teeming with life, they could still be so far away that we would never be able to talk to them.
Furthermore, radio signals disappear with an inverse square law, we probably can't pick our own radio signals at any reasonable distance, so we won't be able to pick aliens even in our own backyard. And if we happen to be in the biggest dump in the galaxy, there won't be aliens in our backyard to begin with. And directed signals are gaining popularity, so even we ourselves are getting more radio silent by the day.
Also, wasn't the paradox partially based on the premise that the aliens would being colonizing the galaxy, and thus spread everywhere in a couple of millions of years? If so, the existence of other aliens in our galaxy might have prevented us from evolving (if they colonized our planet), thus we might only exist because they were not present elsewhere in our galaxy.
And lastly, if the aliens are close enough for us to pick their radio signals, we already have
. That's already too many captured signals for the period that we've been listening.