Regarding the Drake Equation, I believe there are additional factors to consider which make alien contact unlikely. For example:
Perhaps typical aliens are more pragmatic than humans. They could be immediate-goal oriented. “Why should we embark on a voyage that has no payoff for millennia?” Sending Voyager 1 and 2 into interstellar space was really cool, and I’m glad we did it. But, it was pure folly. Maybe aliens don’t engage in folly.
Perhaps typical aliens believe they have everything they could ever want in their own back yard and have no desire to spread their seed beyond their star system. They may be comfortable existing near home and embrace the concept of replacement population. Anything they need, they can make from elements mined from neighboring planets. Why spend bucho alien bucks traveling clear across the galaxy to get the same exact elements and energy sources they have at home? Empire building may be a purely human trait.
Perhaps aliens simply have no curiosity about anything beyond their horizon. Cats are pretty smart and they have a reputation for being curious to a fault. But, they are curious only about things in their domain. I never saw a cat look at the moon and ponder, “I wonder if there are any mice up there?” Bottle-nose dolphin don’t try to torpedo into outer space for a look around. Alien attitude may be, “sure, there’s undoubtedly lot’s of life millions of light years away…but, so what?”
Perhaps intelligent civilizations abound, but we humans are the extroverted outliers. We’re quite monkey-like in our behavior—beating our chests, poking things with sticks, slinging poo all about. “Hey, look at me!”
Typical alien intelligence beings probably evolved on a pathway quite divergent from human evolution. More reserved. More pragmatic. Less showoffy. Less greedy.
This is how I envision first contact with an alien civilization:
Earthling Bob: Greetings, Blurpo. We Earthlings welcome you with open arms. However, we wonder why it has taken so long to make contact with you, or any other advanced civilization in our Milky Way Galaxy. Wassup with that?
Alien Blurpo: Bob, you poor ignorant Earthling. We surveyed your data banks and archives, and laughed our alien asses off. Subspace? Hyperspace? Wormholes? Kardashev Type III civilizations? FTL communication? Duuuude, what the fuck are you guys smoking down there on Earth??? Yeah, sure, we got tech that can blow your collective monkey-minds to oblivion, but you do understand omnipotence is a fairy tale and not a real thing in our universe, don’t you? Hell, we’re just like you, only better in every conceivable way. Don’t you guys know the difference between science and science fiction?