Really well put. All of it.
Like you I'm completely open to the idea of alien life. In fact, the two things I'd love to see before my time on this planet is done (other than the Rams winning enough Super Bowls to be the all-time leader in Lombardis) is proof of extraterrestrial life and a man on Mars.
I don't care if that proof is something as tiny as a molecular fossil, I just want to be alive to see it.
But you're right, there are a lot of things that would have to go right for intelligent aliens to visit us. Think even of trying to find another species in the universe. You're not talking about a needle in a haystack. You're talking about finding a specific grain of sand in a desert. Even that doesn't really do the idea of being found justice.
My brother is a physicist, he is the smartest person I have ever known in my life and will probably ever know. Listening to him describe and explain these concepts is completely mindblowing and so many people who want to believe are just incapable of understanding the magnitude of what it would actually take to make contact with intelligent alien life.
And I have to mention again how much it irks me when people say humans just aren't smart enough or too greedy or barbaric or whatever to achieve interstellar capabilities. It has nothing to do with any of that. It really is just math.