I smell some problems with your ... analysis shall we call it? Civilizations may not be common on Earth, but that's probably because we have only been around that long 10-20k. The real application is using Earth as a reference frame: since the first cell on Earth appeared, has life flourished? Yes it has, it has even started up five times during five mass extinctions. So yes, using Earth as a frame of reference, life should be teeming in the universe. Life certainly has been relentless on Earth, why it can't be relentless elsewhere is an open but logical question.