Here's an alternative resolution to the Fermi paradox: we haven't heard from aliens, because they are communicating in ways that we are insufficiently advanced to listen for.
Analogy: in 1500, even if we'd thought to listen for aliens, we would not have been able to build radio telescopes.
Perhaps any sensible alien civilization communicates using, say, quantum entanglement. The moment we develop this technology and start listening, a cheery message will come from Alpha Centauri: "what took you guys so long?"