As for my thoughts on the paradox? Intelligence like we have it is probably pretty rare, but I believe life overall, complex, glorious, amazingly varied life that shockingly will be a lot like earth life is actually pretty common. I think animal intelligence up to primates is probably not so rare, allowing for differences in evolution based on the history of the planet (impacts, evolutionary choke points, etc).
Human style intelligence with a technological bent is really rare. Too easy to knock yourself back down a few pegs either through self-inflicted actions or the world dealing you a bad hand over and over. We have had massive ices ages and asteroid strikes and super volcanoes and that’s all since humans have been a thing.
We are incredibly fragile in our social constructs, but the good news is we can survive hardships biologically quite well. Humans are here to stay, but we may be Stone Age again for a while… maybe forever. But after the next ice age starts in 12,000 years and finishes in 480,000 more, once we forget we were ever this far along, we will be none the wiser. All evidence will be gone, and we won’t even remember how to look for it.