The question that you linked to does have an answer (it derives from "steer-board"), though this was pointed out in a comment. So that's not a case where it's not possible to answer the question. There is a separate question about the appropriateness of single-word etymologies, so we can leave this particular example. The bigger question is about the notion of a question that can't be answered. There are two existing reasons to close unanswerable questions: (1) unclear what you are asking (therefore we cannot give the answer) and (2) opinion question (again, anything you say is "correct", there is no answer). Once we've excluded questions that do not have an objective answer, we have two kinds of "unanswerable" questions. One is the speculative unknowable question – these might in principle be closable. For example, "what language phylum was spoken by the inhabitants of the Zagros Mountains in 8,000 B.C?". This does refer to an actual fact, but nobody can answer it in lieu of time travel or field work by alien linguists. Although the question does not demand an opinion qua answer, the only responses are going to be either the observation that we can't know, or else some speculative opinion. Conceivably, such questions can be subsumed under the "opinion" reason.
Another class of such questions is the set of "nobody here knows" or perhaps "nobody has figured that out" questions. The Telugu phonemic orthography question probably falls into that category, the problem being that you have to be very familiar with Telugu and Telugu phonology, plus you have to have a good grasp on terminological issues (what exactly does a "phonemic orthography" mean?). We often get existence questions (of the type "are there any Verb-initial ergative languages?"), where we don't want 100 answers saying "I don't know of any" (so how can we distinguish ignorance from an educated claim of non-existence?).
The "any case-marking signed languages" question falls into this class. The problem there is that we have an answer that addresses ASL and BSL, but there are hundreds of other signed languages not reported on (e.g. TSL, KSL for Tanzania, Kenya). Again the question is whether answers should accumulate examples of "not in this language". If yes, then theoretically we might draw at some point the reasonable conclusion that no SL has morphological case marking. If not, we're stuck at knowing about only two languages, unless someone comes up with an example. In other words, existence questions whose answer is "no" are in the neighborhood of "unanswerable".
I do not see what adding a tag would do for us / the question. I don't understand what "filtering-out" needs to be done (for what purpose). Let's assume that there is a goal to have an answer to every question. Some questions can't and shouldn't be answered: unclear ones, opinion ones – these get closed. Also ones that aren't about linguistics. For the other questions, we want answers, not deletion (filtering out). There is a pseudo-tag for identifying those questions, namely the "unanswered" tab at the top. There's no answer for the Slender r question, nor комбинаторная категориальная грамматика, or the don't have verbs question. An alternative to tagging questions is saying "Folks, how about reviewing some of those questions and answering them?". A specific way to get questions answered is to put a bounty on them.
The merit of leaving unanswered questions out there is that they might get answered some day. Like the quantitative metathesis question: as far as I know, this is unique to Ancient Greek; but maybe somebody know an example.
