"Impossible" has a certain appeal, at least for humans; we're all about building that tallest tower and longest bridge, and more recently building our own islands.

I've heard Dyson spheres referred to as a K2 Civ's wonder or vanity project.

  Science advisor:
    Eternal leader, those pesky Alpha Centaurans just completed work on a galactic wonder, the Dyson Sphere! [+1000 energy, +100 habitat]
    Shall we redirect our own Dyson Sphere efforts to a new project?

  Eternal leader:
    Damnit! Yeah fine whatever, let's switch to building a Kemplerer Rosette.