Planck was wrong. And a believer (of sorts). Scientists can be right about the science and woefully misguided on philosophical issues.
All that is reasonable to believe is that life is common in the universe. Civilizations aren't common even on Earth. Of the 3.5 billion years life has been here, civilizations have only been here for 10-20K years. Intelligent life slightly longer. Civilization may not even be a sustainable model of living. There is nothing to indicate that intelligence is a likely adaptation. So statistically speaking, we should not be surrounded by civilizations.
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.