Intelligent life is rare, sure, but there are billions and billions of stars, and therefore solar systems. Supernovas are rare, but we get to see several a year because of the huge numbers we're dealing with.
I think people assume if there is intelligent life in our galaxy (let's also remember there are approximately 200 billion known galaxies in the observable universe, but that's another matter) they assume that intelligent life would have made contact. I doubt it would.
With the recent footage from the US military, it looks like they might already be visiting but just don't want talk to us. To them, we must be imbeciles.
Anyway, a great read and I know nothing abiout science or maths, so hey. Thanks for putting this a topic in such a digestible format.