I take your point, but even if it is true that life is astronomically rare, we are literally talking about astronomy. Life doesn't have to be common for there to be countless worlds with life in our galaxy. In terms of intelligent life, not only must we reckon with the billions upon billions of planets in this galaxy that could host it, but there are also the vast timescales in which it could unfold.
Based on the current trajectory of human civilization, I think the Great Filter [1] theory is increasingly convincing, although that's unfortunate (to put it lightly). If we do manage to avoid destroying ourselves in a sudden cataclysm (such as via nuclear war), we will have to deal with a planet with a destabilized atmosphere, a massively damaged ecosystem, poisoned water and a host of other problems so serious that the word "problem" doesn't seem sufficient.
The timescales required for other advanced technological civilizations to overlap with our own requires that civilizations that go through these periods are able to stop actively destroying their home planet, and then survive the aftermath for a long time afterwards. Whether we are able to do this is very much an open question. We are just a couple of centuries down this road and on balance, I don't think it's going that well.