I do like the equation, but BECAUSE it is mostly a guess and not so rigorous.

The drake equation is not a mathematical proof, neither is it a physical law. It is essentially, a guess.

Maybe that makes you uncomfortable because the guess is in the realm of science. But most of science is just guessing, some educated, and some not.

Scientists and researchers don't like to admit they are guessing, for the most part anyway, because they have this veil of accuracy.

"Look my algorithm found the correct answer 95% of the time"

"Look we made a thing that does a thing for that thing very often"

But remember what the second part of the scientific method is:

Hypothesis.

Now a hypothesis is not always a guess, in the traditional sense of the word. But it's an important part of science.

We observe:

A nail is sticking out of a board

Guess: A hurricane swept through the neighborhood, carrying the nail on the edge of its storm, which eventually found the board and thrust inside of it, and dropped it for me to find. I know this because there was a hurricane in florida and hurricanes are powerful.

Hypothesis: The nail was likely placed with a hammer. I can see marks on the nail the hammer left, I can see imprints of the hammer on the edge of the head. It is likely a type of refuse that was left here on accident.

In this sense, Drake is simply saying,

"Here is what we know about life so far, given our sample of 1 we can eliminate these factors, leaving us with a map of likely candidates"

It is neither accurate, nor precise at the current time. But if a guess is all you have, a guess is all you have.

There is a famous quotation by Newton, although it may have never been said by him:

"No great discovery was ever made without a bold guess"