"Not anymore than A2 + b2 = c2."
This is a stunningly poor analogy.
We know exactly what a and b are physically. We further know that they are the only factors influencing c. And we have a darn good understanding of geometry.
The Drake equation is an assumption, no more, no less, unlike The Pythagorean Theorem you mention.
N = N* fp ne fl fi fc fL
The first two factors are measurable. The next two potentially measurable in the future, though non trivial to ascertain. The rest are, as mentioned, wild assumptions. And as yet another flaw, there is little reason to believe that this equation contains all of the important factors involved in such a determination, even as mere assumptions.
For example, does galactic location make a difference? One would think so, though again this is an assumption. Older stars and those near the galactic center would be by terran standard less likely to harbor life. Should there not be an N1, N2, N3, ... Nn for each generation of star? And also an Nc, Na, No for stars near the center, in the arms, and "other" in our galaxy?
And frankly we know exactly one case of life, let alone intelligent life, developing. The effort to draw conclusions with such a limited data set is bound to fail. Or, to take a reasonable comparison, the Drake Equation is rather the equivalent of studying but one human being and deriving a set of equations explaining all human behaviour.
I don't have a problem with your argument. However, if we don't look we will never know.
IMHO, SETI is a win-win situation. If we are alone (or other races cannot be detected), that in itself is extremely profound. If we are not, that is equally profound. So SETI in either case will give us a better understanding of our place in this universe.