"The Drake equation basically says what anybody who has looked up at the night sky knows intuitively: there are a lot of stars out there, and it's extremely unlikely that we're all by ourselves."
Further reinforcing your core point, it can also tell you that we are. You don't have to be that painfully conservative with the numbers to come with one or fewer per galaxy. For instance, 50% of stars having planets may be a brutal overestimate, a lot of stars are in multi-star systems or other situations in which there are no stable orbits, resulting in any initial planets getting ejected very quickly if they form at all. 2 Earth-like planets per star is a bold statement, depending on the exact definition of "Earth-like", we only have one in our system and if you read past the propaganda in the planet finding press releases they aren't coming up with all that many other "Earth like" planets yet. Yes, that's because they still can't see them, but the press releases convey a false sense of how the search is going when they do things like call a planet with a surface gravity of 3 or 4 G and a surface temperature beyond rock's liquification point a "Super-Earth". 10000 years is a bold estimate for how long a civ will be around and communicating, certainly. I actually am against the self-loathing that some circles find fashionable but 10,000 years is a long time. I consider these numbers generous and it still only comes up with 10.
It's missing some terms, too. Irregular galaxies [1], approximately 25% of the galaxies out there, are thought to be entirely unable to support complex life because basically all the stars in such galaxies will take a system through a region of the galaxy with too much radiation and sterilize the planets every few tens of millions of years. I mean this only as an example, you can go on naming more fairly reasonable criteria that eliminate half or more stars from contention for quite a while (star types, star galactic orbits, other galaxy attributes, even before we get to planets we can eliminate a lot).
To brutally abuse notation, the night sky is O(n^3) in size, if the probabilities of developing civilization are O(2^n)-type it doesn't matter how large the sky is. Big numbers fall fast when you multiply independent probabilities together, and it's not sophistication to just give up and declare there must be a lot of other civilizations out there; it's still a mathematical copout. We don't know.
[1]: http://en.wikipedia.org/wiki/Irregular_galaxy