Frame Challenge (AKA oblique answers) are necessary and acceptable
After crawling around on a few sites, reading lots of posts, thinking about what they said, re-framing that for the context of CSE, and thinking some more, I've distilled some informative posts from elsewhere for our consideration.
From hither and yon: What they do
SevenSidedDie, a moderator on Role-playing Games, answered the Meta Stack Exchange question Does Stack Exchange allow for answers which question the validity or stance of the original question? with some of the wisdom his site had gained with "frame challenges."
However, our wisdom around frame challenges comes with one big, huge caveat: they are not guaranteed to be right or agreed with by the community. For one, you might be wrong; for two, even when right it takes a whole level more of writing and persuasion skill to pull off a frame challenge than it takes for a straightforward answer. Our experience is that frame challenges are sometimes extremely good answers, but when they're ever so slightly less than stellar, they get murdered in the voting.
But like calling a trick shot in a game of pool, you increase the risk and reward when you do it. The normal voting mechanism will decide whether you've succeeded, and as always with votes, the farther you go out on a limb, the more the voting is going to be polarised.
The Role-playing Games site's handling of such answers seems to be rooted in their meta post How do we handle a desire to challenge the frame of a question? and its answer. In that answer there are two portions I find significant.
First is a set of guidelines to consider when actually posting a frame challenge, which seem to be valid, in the main, here on CSE as well.
You need to be careful when challenging the frame of a question - the line between that and threadcrapping can be a narrow one. You should:
Provide your critique as part of an otherwise legitimate answer. (This isn't strictly required, but we very strongly recommend it. Sometimes declining to answer the question and instead going straight to a frame challenge — e.g. “don't do that at all” — is the right answer, but it's also risky and liable to backfire. This is a judgement call for the author and voters to handle.)
Do it carefully and support your challenge - "I prefer different things" is not really a good reason, remember this isn't a forum and the goal of the site is to solve people's problems, not to wave our own personal freak flag around.
Don't get upset if you get voted down because the community thinks you overstepped your bounds. You know you're taking a risk by doing it instead of just answering their question.
The first point can be situationally debated. There arise questions where providing an otherwise legitimate answer is either not practical, or inadvisable. For a related question, Is “Don't do it” a valid answer? on Meta Stack Exchange, Shog9♦ posted a comment on one of the answers.
On the one hand, i can sympathize: i asked a question looking for legitimate uses for a much-maligned language feature, and was quickly slammed with replies urging against its use in any situation. Not very helpful... On the other hand, i've seen questions asking for help doing things that are unkind or flat-out dangerous to others. I don't want to answer these questions and then warn against using the technique presented in my answer - that's handing a toddler a loaded gun and then asking him not to shoot anything! I'd rather convince him of the danger and help him avoid the entire situation. – Shog9♦ Jul 24 '09 at 17:26
As the RPG states, "something about the question frame makes answering the question invalid and the only tenable answer is mu."
The second point in the RPG answer which I find particularly relevant to our site is about on-topic vs. off-topic for an answer.
Also note that if the question asker specifically addresses your concern proactively, you are pretty much off topic. People legitimately disagree, and you are not helping the person if you are going down a path they have explicitly stated as off topic. For example, in my question on How do you help players not focus on the rules?, I proactively noted that I understood not everyone wants that playstyle but that is not relevant and I want answers from that frame. Of course, if a questioner asks a question and rules out what everyone considers to be the sensible paths - then they get no good answers, and they reap what they sow.
This is a point that, as I understand it, the Parenting site will not accept. Especially on subjective issues. Even for objective, verifiable factual errors their preference is to use comments, or editing, to correct the question. On the opposite end of the spectrum is Interpersonal Skills, where it seems that even an answer that goes against the explicitly rejected options of the OP are at least considered, it not completely accepted.
My take: Suggestions for CSE
Here on CSE I believe that our approach to that aspect ought to be reasonably strict in complying with the OP's explicitly excluded options. There are many factors which could make options unavailable to the OP that are not stated in the question. School/District/State guidelines, policies, or resources might require somethings that we don't like, or disallow other things we think should be mandatory. Expecting the OP to cover every reason why some options are not available could lead to very long questions, and add nothing to the question's value, now or in the future. If the OP says, for example, that Java is not an option, or that using Cloud-based systems is not part of the solution, then an answer that uses the the excluded factors is Not An Answer. Likewise, when something is stated as needed by the OP, an answer that does not meet that need is also Not An Answer.
When the OP has set a limitation or a requirement that seems counter to a good solution, comments may be used to clarify the significance of that in possible answers. It's possible that No Java is based on their not knowing, or not liking Java, and they agree to consider it after all, and edit the question accordingly. Absent such clarification, or worse, in spite of the reverse - emphasis of the strictures - any answer that follows that path is really Not An Answer.
One possible justification that has been offered for providing an answer contrary to the OP's limitations is that the answers are also for the future users, and random Google searchers, and while it might not be acceptable in the OP's position, it could work for others. I've learned that the best lies are 99% true, with only 1% falsehood. I think the same analysis applies to that justification. If the user creating an answer contrary to the OP's established boundaries really believes what they have to say is useful, SE provides a way to say it: a "Self-Answered" question. Self-answered questions allow any user to share any knowledge they possess. There's no need to hijack a question which that knowledge does not legitimately apply to.
Within some set of guidelines, either akin to the RPG style, the IPS style, or something in between, which we establish and set forth for reference, I believe we do need to accept frame challenge answers in some cases. I also think the user posting a frame challenge answer should recognize the risks in doing so, and accept the down votes that happen when it does not go well.
How I evaluate a Frame Challenge answer
When I read an answer that is "Don't do that" I look for the reasoning, rationale, and justification for that position, and I look for an explanation of why the user thinks those reasons apply to this question, what the user thinks the problem really is, and for a really good solution within the frame they propose using for the problem. I'm looking for the sales pitch and the proof. Then, if I'm convinced the challenge is valid, I'll look at the new solution. That's where my vote will be decided. I don't down vote as much as some, mostly because users often see a DV as personal and I'm not into causing such feelings in others. My DV's on answers go to extreme cases where I think there is a serious problem with the answer, or it's just plain basura and I'd toss it into the dustbin if I had one. Flags, however, I will issue with a higher priority, and a lower threshold.