I've been running into a lot of situations like this:
OP asks how to find a solution to an elementary equation (in the sense of being written in elementary functions), but without an answer that can really be given in an exact form, something like solving $3^{x} + \frac{x}{5} = 2.7^{x}$, something that cannot be solved explicitly, but can be solved numerically. Somebody responds by suggesting that one finagle it a bit, and then appeal to Banach's fixed point theorem. This is of course a sound method, and will work (assuming such finagling is possible), but it doesn't strike me as very appropriate, because the question strikes me as a homework-type problem, or at least one that was encountered in or inspired by a class. I see this problem and think, "This cat's going through a pre-calc, college algebra course," so it seems sensible that a good answer would use the tools the student has at her disposal, and though I cannot speak for everybody when I say this, it was my understanding that something like Banach's fixed point theorem would not be encountered until a good bit later in a math education (for better or worse). Of course, the OP could look up "Banach fixed point theorem" and see what it says, maybe even understand the proof, but it would not be of much aid in the actual class.
It reminds me somewhat of a calculus class I took, and we were given a test covering Taylor expansions, and we'd been told to derive the Taylor expansion for $\exp$. I said that we could do this by understanding $\exp$ as the unique solution to the differential equation given by $f' = f, f(0) = 1$. I got no credit, and when I asked him about it after the fact, he asked (and probably rightly so) how I knew those conditions had only one solution, to which I mumbled something along the lines of, "Because you said so once." Obviously I could not answer his inquiry satisfactorily, and so I did not get credit on the exam. But even if I had given a complete proof that my answer worked, going through to show that any two solutions to $f' = f$ could only differ by a multiplicative constant, it still would've missed the point, because the goal of the question was to test my familiarity with Taylor expansions, and my method didn't do it.
Similarly, using Banach to answer a pre-calc question sounds not only like overkill, but moreover sounds like taking a foreign and undiscussed result/method that the student may very likely not really grasp, and missing the goal of working some other more elementary technique, and so to say, "Appeal to Banach" might be a sound and workable method, it doesn't meet the OP's needs.
So my question is, does MSE etiquette have a mechanism for this? Is there a way to determine the appropriate amount of "technology" for a problem? Is there a way to express to another answer that you think their answer is inappropriate for the OP and their needs? Perhaps should there be?